## Metrics

## Announcements & Documents

Dear All,

Write at least two problems and solutions about each of the subjects below. The homework must be prepared in Latex or Microsoft Word (docx) format. Equations must be written using the equation editor or MathType in Word or Latex. Equations in photo format are not accepted. Homeworks consisting of all the same examples and the same solutions will not be accepted

Homework must be uploaded to the YTU online system in a Microsoft Word document. The deadline is 12.06.2023 till 23:59 (Final exam day). Assignment after the deadline will not be accepted.

Midterm Exam : %30, Percentage of Homework: %30, Final Exam: %40

1. First-order partial differential equations (Integral Curves)

2. First-order partial differential equations (Integral Surfaces)

3. First-order partial differential equations (Vector Fields)

4. First-order partial differential equations (Lagrange Charpit Method)

5. Second order PDEs, Separation of variables method

6. Second Order Linear PDEs (Canonical Forms)

7. Second Order Linear PDEs (D’Alembert Formula and solution method)

8. Parabolic (Heat) equation (Uniqueness, Energy method)

9. Parabolic (Heat) equation (Maximum principle)

10. Parabolic (Heat) equation (Fundamental solution)

11. Laplace’s equations (Fundamental Solutions)

12. Poisson’s equation (Fundamental solution)

13. Poisson’s equation (Green functions)

14. Initial and boundary value problems for wave equation

15. Wave equations (Energy estimates)

**Dear All,**

**Write at least two problems and solutions about each of the subjects below. The homework must be prepared in Latex or Microsoft Word (docx) format. Equations must be written using the equation editor or MathType in Word or Latex. Equations in photo format are not accepted. Homeworks consisting of all the same examples and the same solutions will not be accepted**

**Homework must be uploaded to the YTU online system in a Microsoft Word document. The deadline is 12.06.2023 till 23:59 (Final exam day). Assignments after the deadline will not be accepted.**

**Midterm Exam : %30, Percentage of Homework: %30, Final Exam: %40**

** **

**1. First-order partial differential equations (Integral Curves)**

**2. First-order partial differential equations (Integral Surfaces)**

**3. First-order partial differential equations (Vector Fields)**

**4. First-order partial differential equations (Lagrange Charpit Method)**

**5. Second order PDEs, Separation of variables method**

**6. Second Order Linear PDEs (Canonical Forms)**

**7. Second Order Linear PDEs (D’Alembert Formula and solution method)**

**8. Parabolic (Heat) equation (Uniqueness, Energy method)**

**9. Parabolic (Heat) equation (Maximum principle)**

**10. Parabolic (Heat) equation (Fundamental solution)**

**11. Laplace’s equations (Fundamental Solutions)**

**12. Poisson’s equation (Fundamental solution)**

**13. Poisson’s equation (Green functions)**

**14. Initial and boundary value problems for wave equation**

**15. Wave equations (Energy estimates)**

Dear All,

I have attached the PDE lecture notes. The password will be shared by email through OBS.

Best

PDE Lecture Notes.rar

Dear All,

MAT2171 Differential Equations I course syllabus are attached below.

Best regards

MAT2171_2021_Güz.pdf## Education Information

2007 - 2011

2007 - 2011###
**Doctorate**

#### Bursa Uludağ University, Faculty Of Arts And Scıences, Turkey

1996 - 2000

1996 - 2000###
**Undergraduate**

#### Uludağ Üniversitesi, Fen Edebiyat Fakültesi, Matematik, Turkey

## Dissertations

2011

2011###
**Doctorate**

#### Lokal olmayan hiperbolik problemler için kararlı fark şemaları

##### Bursa Uludağ University, Fen Bilimleri Enstitüsü, Fen Bilimleri Enstitüsü

## Foreign Languages

C2 Mastery

C2 Mastery###
** English**

## Research Areas

**Mathematics**

**Differential Equations**

**Functional Equations**

**Functional Analysis**

**Fourier Analysis**

**Integral Transformations, Computational Calculation**

**Partial Differential Equations**

**Numerical Analysis**

**Natural Sciences**

## Academic Titles / Tasks

2018 - Continues

2018 - Continues###
**Associate Professor**

#### Yildiz Technical University, Faculty Of Arts & Science, Department Of Mathemeatics

2012 - 2018

2012 - 2018###
**Assistant Professor**

#### Yildiz Technical University, Faculty Of Arts & Science, Department Of Mathemeatics

## Advising Theses

2023

2023###
**Postgraduate**

####
**Mathematical modelling methodology and a traffic model by data analysis and machine learning **

#### Yıldırım Ö. (Advisor)

##### S.DEMİR(Student)

2021

2021###
**Doctorate**

####
**On solvability of nonlinear coupled wave systems arising in DNA dynamics **

#### Yıldırım Ö. (Advisor)

##### M.UZUN(Student)

2021

2021###
**Postgraduate**

####
**Lie Symmetry Analysis of the coupled system of sine-Gordon equations **

#### Yıldırım Ö. (Advisor)

##### M.MENDİ(Student)

2019

2019###
**Doctorate**

####
**Application of Lie Symmetries to Difference Equations and Boundary Value Problems **

#### Yıldırım Ö. (Advisor)

##### S.ÇAĞLAK(Student)

2014

2014###
**Postgraduate**

####
**High Order Stable Difference Schemes for Multipoint Nonlocal Boundary Value Problems for Hyperbolic Equations **

#### Yıldırım Ö. (Advisor)

##### M.Uzun(Student)

## Published journal articles indexed by SCI, SSCI, and AHCI

2023

2023###
**On Exact Solutions of Some Space–Time Fractional Differential Equations with M-truncated Derivative**

#### Özkan A., Özkan E. M., Yildirim O.

##### FRACTAL AND FRACTIONAL , vol.2023, no.7, pp.1-14, 2023 (SCI-Expanded)

2020

2020###
**Weak solvability of the unconditionally stable difference scheme for the coupled sine-Gordon system**

#### YILDIRIM Ö., UZUN M.

##### NONLINEAR ANALYSIS-MODELLING AND CONTROL , vol.25, no.6, pp.997-1014, 2020 (SCI-Expanded)

2019

2019###
**Lie point symmetries of difference equations for the nonlinear sine-Gordon equation**

#### Yıldırım Ö., Caglak S.

##### PHYSICA SCRIPTA , vol.94, 2019 (SCI-Expanded)

2017

2017###
**On Fourth-Order Stable Difference Scheme for Hyperbolic Multipoint NBVP**

#### Yıldırım Ö., Uzun M.

##### NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION , vol.38, pp.1305-1324, 2017 (SCI-Expanded)

2015

2015###
**On the numerical solutions of high order stable difference schemes for the hyperbolic multipoint nonlocal boundary value problems**

#### Yıldırım Ö., Uzun M.

##### APPLIED MATHEMATICS AND COMPUTATION , vol.254, pp.210-218, 2015 (SCI-Expanded)

2015

2015###
**On Third Order Stable Difference Scheme for Hyperbolic Multipoint Nonlocal Boundary Value Problem**

#### Yıldırım Ö., Uzun M.

##### DISCRETE DYNAMICS IN NATURE AND SOCIETY , 2015 (SCI-Expanded)

2013

2013###
**On the numerical solution of hyperbolic IBVP with high-order stable finite difference schemes**

#### Ashyralyev A., Yıldırım Ö.

##### BOUNDARY VALUE PROBLEMS , 2013 (SCI-Expanded)

2013

2013###
**On Stability of a Third Order of Accuracy Difference Scheme for Hyperbolic Nonlocal BVP with Self-Adjoint Operator**

#### Ashyralyev A., Yıldırım Ö.

##### ABSTRACT AND APPLIED ANALYSIS , 2013 (SCI-Expanded)

2012

2012###
**A Note on the Second Order of Accuracy Stable Difference Schemes for the Nonlocal Boundary Value Hyperbolic Problem**

#### Ashyralyev A., Yıldırım Ö.

##### ABSTRACT AND APPLIED ANALYSIS , 2012 (SCI-Expanded)

2011

2011###
**Stable difference schemes for the hyperbolic problems subject to nonlocal boundary conditions with self-adjoint operator**

#### Ashyralyev A., Yildirim O.

##### APPLIED MATHEMATICS AND COMPUTATION , vol.218, pp.1124-1131, 2011 (SCI-Expanded)

2010

2010###
**ON MULTIPOINT NONLOCAL BOUNDARY VALUE PROBLEMS FOR HYPERBOLIC DIFFERENTIAL AND DIFFERENCE EQUATIONS**

#### Ashyralyev A., Yildirim O.

##### TAIWANESE JOURNAL OF MATHEMATICS , vol.14, pp.165-194, 2010 (SCI-Expanded)

## Articles Published in Other Journals

2021

2021###
**On the Lie symmetries of the boundary value problems for differential and difference sine-Gordon equations**

#### YILDIRIM Ö., Caglak S.

##### BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS , vol.102, no.2, pp.142-153, 2021 (ESCI)

2019

2019###
**On stable high order difference schemes for hyperbolic problems with the Neumann boundary conditions**

#### Yıldırım Ö.

##### International Journal of Optimization and Control: Theories and Applications , vol.9, pp.60-72, 2019 (Scopus)

2007

2007###
**A Note On The Numerical Solutions Of Hyperbolic Partial Differential Equations**

#### Yıldırım Ö., Ashyralyev A.

##### Sakarya Universitesi Fen Edebiyat Dergisi , vol.9, no.2, pp.33-49, 2007 (Peer-Reviewed Journal)

## Refereed Congress / Symposium Publications in Proceedings

2022

2022###
**On the weak solution of third order of accuracy difference scheme for coupled sine-Gordon equations**

#### YILDIRIM Ö., Batıbay Yumurtacı B.

##### Sixth International Conference on Analysis and Applied Mathematics, Almaty, Kazakhstan, 31 October - 06 November 2022

2022

2022###
**Mathematical modelling of traffic with regression analysis and machine learning**

#### YILDIRIM Ö., DEMİR S.

##### Sixth International Conference on Analysis and Applied Mathematics, Almaty, Kazakhstan, 31 October - 06 November 2022

2020

2020###
**On the Asymptotic Formula for the Solution of Nonlocal Boundary Value Perturbation Problems for Hyperbolic Equations**

#### Ashyralyev A., YILDIRIM Ö.

##### 5th International Conference on Analysis and Applied Mathematics (ICAAM), Mersin, Turkey, 23 - 30 September 2020, vol.2325

2020

2020###
**NUMERICAL ANALYSIS OF THE NONLINEAR WAVE SYSTEMS BY A NOVEL ITERATIVE METHOD**

#### YILDIRIM Ö., UZUN M.

##### ICFAS 2020, 06 October 2020

2020

2020###
**On Convergence of Second Order of AccuracyFinite-Dierence Scheme for Coupled sine-GordonEquations**

#### YILDIRIM Ö., UZUN M.

##### CMMSE’20, ROTA CADIZ, Spain, 3 - 09 July 2020

2019

2019###
**On unique solvability of nonlinear coupled systems**

#### Yıldırım Ö., Uzun M.

##### International Conference of Mathematical Sciences (ICMS 2019), İstanbul, Turkey, 4 - 08 September 2019, pp.1-10

2019

2019###
**Symmetry analysis of the discrete nonlinear boundary value problems for the wave equation**

#### Yıldırım Ö., Çağlak S.

##### International Conference of Mathematical Sciences (ICMS 2019), İstanbul, Turkey, 4 - 08 September 2019, pp.1-10

2019

2019###
**On Weak Solvability of Coupled Systems**

#### Yıldırım Ö., Uzun M.

##### 3. International Conference on Mathematics: An Istanbul Meeting for World Mathematicians, İstanbul, Turkey, 3 - 05 July 2019

2019

2019###
**A COMPOSITE NUMERICAL METHOD ON THE SOLUTION OF COUPLED SINE-GORDON EQUATIONS BASED ON THE FIXED POINT THEORY**

#### Yıldırım Ö., Uzun M.

##### Banach Spaces and their Applications, Lviv, Ukraine, 26 - 29 June 2019

2019

2019###
**ON GENERALIZED SOLUTIONS OF NONLINEAR SYSTEMS**

#### Yıldırım Ö., Uzun M.

##### 6th International Congress on Fundamental and Applied Sciences 2019 (ICFAS2019), Tirane, Albania, 18 - 20 June 2019, pp.146

2019

2019###
**Lie Point Symmetries of Difference Equation**

#### Yıldırım Ö., Çağlak S.

##### INTERNATIONAL CONFERENCE on MATHEMATICAL ADVANCES and APPLICATIONS (ICOMAA2019), İstanbul, Turkey, 3 - 05 May 2019, pp.1-5

2019

2019###
**A Note on the Numerical Solution of Coupled Klein-Gordon Equations**

#### YILDIRIM Ö., UZUN M.

##### 3rd International Conference of Mathematical Sciences (ICMS), İstanbul, Turkey, 4 - 08 September 2019, vol.2183

2018

2018###
**Invariant difference schemes for sine-Gordon equations, Fourth International Conference on Analysis and Applied Mathematics**

#### Yıldırım Ö., Çağlak S.

##### Fourth International Conference on Analysis and Applied Mathematics, Lefkoşa, Cyprus (Kktc), 6 - 09 September 2018, pp.1-10

2018

2018###
**NUMERICAL SOLUTION OF HYPERBOLIC EQUATIONS WITH NONLOCAL BVPs**

#### Yıldırım Ö., Uzun M.

##### 5th International Congress on Fundamental and Applied Sciences 2018 (ICFAS2018), Skopje, Macedonia, 18 - 22 June 2018, pp.212

2018

2018###
**On the Numerical Solution of Nonlinear System of Coupled Sine-Gordon Equations**

#### Yıldırım Ö., Uzun M., Altun O.

##### 4th International Conference on Analysis and Applied Mathematics (ICAAM), Mersin, Turkey, 6 - 09 September 2018, vol.1997

2017

2017###
**Unique Solvability Results on Boundary Value Problems for Semilinear Hyperbolic Equations**

#### Yıldırım Ö., Uzun M.

##### International Congress on Fundamental and Applied Sciences, Sarajevo, Bosnia And Herzegovina, 21 - 25 August 2017, pp.78

2017

2017###
**A Note on the Exact Solution Methods for Nonlinear PDEs**

#### Yıldırım Ö., Uzun M.

##### International Congress on Fundamental and Applied Sciences 2017 (ICFAS2017), Sarajevo, Bosnia And Herzegovina, 21 August 2017, pp.78

2017

2017###
**On the Existence and Uniqueness of Solutions to Nonlinear Wave Equations**

#### Yıldırım Ö., Uzun M.

##### International Conference on Mathematics and Mathematics Education, Şanlıurfa, Turkey, 11 - 13 May 2017, pp.549-550

2016

2016###
**On the analytical solution methods for sine Gordon equation**

#### Yıldırım Ö., Uzun M.

##### ICAAM 2016, Almati, Kazakhstan, 7 - 10 September 2016

2016

2016###
**On the numerical solution of sine Gordon equation**

#### Yıldırım Ö., Uzun M.

##### ICAAM 2016, Almati, Kazakhstan, 7 - 10 September 2016

2016

2016###
**On stable difference schemes for multipoint NBVP of the hyperbolic type**

#### Yıldırım Ö., Uzun M.

##### International Congress on Fundamental and Applied Sciences (ICFAS 2016), İstanbul, Turkey, 22 August 2016, pp.122

2016

2016###
**On Stability of Fourth Order of Accuracy Difference Scheme for Hyperbolic Multipoint NBVP with Neumann Conditions**

#### Yıldırım Ö., Uzun M.

##### International Conference on Mathematics and Mathematics Education (ICMME 2016), Elazığ, Turkey, 12 - 15 May 2016, pp.392-393

2016

2016###
**On stability of difference schemes for hyperbolic multipoint NBVP with Neumann conditions**

#### YILDIRIM Ö., UZUN M.

##### 3rd International Conference on Analysis and Applied Mathematics (ICAAM), Almaty, Kazakhstan, 7 - 10 September 2016, vol.1759

2015

2015###
**A Note on the Numerical Solution of Multipoint Nonlocal Boundary Value Hyperbolic Problem with Neumann Conditions**

#### Yıldırım Ö., Uzun M.

##### International Conference on Analysis and Mathematical Modelling (ICAAMM2015), İstanbul, Turkey, 08 June 2015, pp.200

2015

2015###
**On stability of high order difference schemes for hyperbolic multipoint nonlocal boundary value problem**

#### Yıldırım Ö., Uzun M.

##### AMS- EMS- SPM International Meeting 2015, Porto, Portugal, 10 - 13 June 2015, pp.75

2014

2014###
**On third order of accuracy stable difference scheme for multipoint nbvp of the hyperbolic type**

#### Yıldırım Ö., Uzun M.

##### Second International Conference on Analysis and Applied Mathematics (ICAAM 2014), Simkent, Kazakhstan, 11 - 13 September 2014, pp.90-91

2014

2014###
**On fourth order of accuracy stable difference scheme for multipoint nbvp of the hyperbolic type**

#### Yıldırım Ö., Uzun M.

##### ICAAM 2014, Simkent, Kazakhstan, 11 - 13 September 2014

2014

2014###
**High order of accuracy stable difference schemes for the approximate solution of the multipoint NBVP for the hyperbolic equation**

#### YILDIRIM Ö., UZUN M.

##### 2nd International Conference on Analysis and Applied Mathematics (ICAAM), Shymkent, Kazakhstan, 11 - 13 September 2014, vol.1611, pp.305-309

2013

2013###
**ON THE STABILITY OF HIGH ORDER OF ACCURACY DIFFERENCE SCHEMES FOR NONLOCAL BOUNDARY VALUE PROBLEMS WITH SELF ADJOINT OPERATOR**

#### Yıldırım Ö., Ashyralyev A.

##### Differential Equations. Function Spaces. Approximation Theory, Novosibirsk, Russia, 18 - 24 August 2013, pp.434-435

2013

2013###
**On stability of a fourth order of accuracy difference scheme for nonlocal BVPs with self-adjoint operator**

#### YILDIRIM Ö.

##### International Conference on Applied analysis and Mathematical Modelling (ICAAMM2013), 01 June 2013

2012

2012###
**High Order Accurate Difference Schemes for Hyperbolic IBVP**

#### Ashyralyev A., Yildirim O.

##### 5th International Conference Numerical Analysis and Applications (NAA), Lozenetz, Bulgaria, 15 - 20 June 2012, vol.8236, pp.174-181

2012

2012###
**Stable High Order of Accuracy Difference Schemes for Hyperbolic IBVP**

#### Ashyralyev A., Yıldırım Ö.

##### International Conference on Applied Analysıs and Algebra (ICAAA 2012), İstanbul, Turkey, 20 - 24 June 2012, pp.213

2012

2012###
**High Order of Accuracy Stable Difference Schemes for Numerical Solutions of NBVP for Hyperbolic Equations**

#### Ashyralyev A., Yildirim O.

##### 1st International Conference on Analysis and Applied Mathematics (ICAAM), Gümüşhane, Turkey, 18 - 21 October 2012, vol.1470, pp.84-87

2011

2011###
**Second Order of Accuracy Stable Difference Schemes for Hyperbolic Problems Subject to Nonlocal Conditions with Self-Adjoint Operator**

#### Ashyralyev A., Yildirim O.

##### International Conference on Numerical Analysis and Applied Mathematics (ICNAAM), Halkidiki, Greece, 19 - 25 September 2011, vol.1389

2009

2009###
**A Note on Hyperbolic Equations with Nonlocal Boundary and Dirichlet-Neumann Conditions**

#### Ashyralyev A., Yıldırım Ö.

##### International Conference of Mathematical Sciences (ICMS 2009), İstanbul, Turkey, 4 - 10 August 2009, pp.1

2007

2007###
**A NOTE ON THE NUMERICAL SOLUTIONS OF HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS**

#### Yıldırım Ö., Ashyalyev A.

##### II. Türk dünyası matematik sempozyumu, (04-07 Temmuz 2007), Sakarya, Turkey, 4 - 07 July 2007, pp.1-10

## Supported Projects

2022 - 2023

2022 - 2023###
**WEAK SOLUTIONS OF THIRD ORDER OF ACCURACY DIFFERENCE SCHEME FOR NONLINEAR SYSTEM OF WAVE EQUATIONS
(DOĞRULUĞUN ÜÇÜNCÜ DÜZEYDEN ZAYIF ÇÖZÜMLERİ DOĞRUSAL OLMAYAN SİSTEM İÇİN FARK ŞEMASI DALGA DENKLEMLERİ)**

#### Project Supported by Higher Education Institutions

##### YILDIRIM Ö. (Executive), BATIBAY YUMURTACI B.

2021 - 2023

2021 - 2023###
**MATHEMATICAL MODELLING METHODOLOGY AND A TRAFFIC MODEL BY DATA ANALYSIS AND MACHINE LEARNING**

#### Project Supported by Higher Education Institutions

##### YILDIRIM Ö. (Executive), Demir S.

2017 - 2022

2017 - 2022###
**Investigation and Mathematical Analysis of Avant-garde Disease Control via Mosquito Nano-Tech-Repellents**

#### TÜBİTAK - AB COST Project

##### Yıldırım Ö., Gaffarı P.(Executive), Grancaric A. M.(Executive)

2016 - 2021

2016 - 2021###
**ON SOLVABILITY OF NONLINEAR COUPLED WAVE SYSTEMS ARISING IN DNA DYNAMICS
(DNA Dinamiğinde Ortaya Çıkan Nonlineer Bağlı Dalga Denklem Sistemlerinin Çözülebilirliği Üzerine)**

#### Project Supported by Higher Education Institutions

##### YILDIRIM Ö. (Executive), UZUN M.

2019 - 2020

2019 - 2020###
**Lie Simetrilerinin Diferansiyel ve Fark Denklemlerine Uygulanması (Application of Lie Symmetries to Differential and Difference Equations) **

#### Project Supported by Higher Education Institutions

##### Yıldırım Ö. (Executive), Çağlak S.

## Activities in Scientific Journals

2017 - 2020

2017 - 2020###
**Applied and Computational Mathematics**

#### Committee Member

## Memberships / Tasks in Scientific Organizations

2014 - Continues

2014 - Continues###
**European Mathematical Society (EMS)**

#### Member

## Scientific Refereeing

June 2017

June 2017###
**Thermal Science**

#### SCI Journal

June 2017

June 2017###
**Numerical Mathematics Theory Methods and Applications**

#### SCI Journal

March 2017

March 2017###
**FILOMAT**

#### SCI Journal

February 2017

February 2017###
**FILOMAT**

#### SCI Journal

November 2016

November 2016###
**Numerical Functional Analysis and Optimization**

#### SCI Journal

August 2016

August 2016###
**Springer plus**

#### SCI Journal

July 2014

July 2014###
**Applied Mathematics & Information Sciences**

#### SCI Journal

## Tasks In Event Organizations

Mayıs 2019

Mayıs 2019### INTERNATIONAL CONFERENCE on MATHEMATICAL ADVANCES and APPLICATIONS (ICOMAA2018)

#### Scientific Congress

##### Yıldırım Ö.

##### İstanbul, Turkey

Mayıs 2019

Mayıs 2019### INTERNATIONAL CONFERENCE on MATHEMATICAL ADVANCES and APPLICATIONS (ICOMAA2019)

#### Scientific Congress

##### Yıldırım Ö.

##### İstanbul, Turkey

Eylül 2018

Eylül 2018### International Conference on Analysis and Applied Mathematics (ICAAM 2018)

#### Scientific Congress

##### Yıldırım Ö.

##### Lefkoşa, Cyprus (Kktc)

Eylül 2016

Eylül 2016### International Conference on Analysis and Applied Mathematics (ICAAM 2016)

#### Scientific Congress

##### Yıldırım Ö.

##### Almati, Kazakhstan

Ağustos 2016

Ağustos 2016### International Congress on Fundamental and Applied Sciences (ICFAS 2016)

#### Scientific Congress

##### Yıldırım Ö.

##### İstanbul, Turkey

Haziran 2015

Haziran 2015### INTERNATIONAL CONFERENCE ON APPLIED ANALYSIS AND MATHEMATICAL MODELING (ICAAMM 2015)

#### Scientific Congress

##### Yıldırım Ö.

##### İstanbul, Turkey

Eylül 2014

Eylül 2014