Announcements & Documents
PDE Project Homework
Homework
6/11/2023
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)
PDE Homework
Homework
4/18/2023
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)
Homeworks_Spring_2023_YTU.pdf
PDE Lecture Notes
Lecture Note
4/13/2023
Dear All,
I have attached the PDE lecture notes. The password will be shared by email through OBS.
Best
PDE Lecture Notes.rar
MAT2171 Differential Equations I Syllabus
Announcement
10/6/2021
Dear All,
MAT2171 Differential Equations I course syllabus are attached below.
Best regards
MAT2171_2021_Güz.pdf
Linear Algebra Course Contents MAT1320
Lecture Note
2/6/2020
Mathematics 1 Course Contents MAT1071
Lecture Note
2/6/2020
Education Information
2007 - 2011
2007 - 2011Doctorate
Bursa Uludağ University, Faculty Of Arts And Scıences, Turkey
1996 - 2000
1996 - 2000Undergraduate
Uludağ Üniversitesi, Fen Edebiyat Fakültesi, Matematik, Turkey
Dissertations
2011
2011Doctorate
Lokal olmayan hiperbolik problemler için kararlı fark şemaları
Bursa Uludağ University, Fen Bilimleri Enstitüsü, Fen Bilimleri Enstitüsü
Foreign Languages
C2 Mastery
C2 MasteryEnglish
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 - ContinuesAssociate Professor
Yildiz Technical University, Faculty Of Arts & Science, Department Of Mathemeatics
2012 - 2018
2012 - 2018Assistant Professor
Yildiz Technical University, Faculty Of Arts & Science, Department Of Mathemeatics
Advising Theses
2023
2023Postgraduate
Mathematical modelling methodology and a traffic model by data analysis and machine learning
Yıldırım Ö. (Advisor)
S.DEMİR(Student)
2021
2021Doctorate
On solvability of nonlinear coupled wave systems arising in DNA dynamics
Yıldırım Ö. (Advisor)
M.UZUN(Student)
2021
2021Postgraduate
Lie Symmetry Analysis of the coupled system of sine-Gordon equations
Yıldırım Ö. (Advisor)
M.MENDİ(Student)
2019
2019Doctorate
Application of Lie Symmetries to Difference Equations and Boundary Value Problems
Yıldırım Ö. (Advisor)
S.ÇAĞLAK(Student)
2014
2014Postgraduate
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
2023On 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
2020Weak 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
2019Lie point symmetries of difference equations for the nonlinear sine-Gordon equation
Yıldırım Ö., Caglak S.
PHYSICA SCRIPTA
, vol.94, 2019 (SCI-Expanded)
2017
2017On 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
2015On 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
2015On 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
2013On the numerical solution of hyperbolic IBVP with high-order stable finite difference schemes
Ashyralyev A., Yıldırım Ö.
BOUNDARY VALUE PROBLEMS
, 2013 (SCI-Expanded)
2013
2013On 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
2012A 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
2011Stable 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
2010ON 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
2021On 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
2019On 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
2007A 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
2022On 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
2022Mathematical 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
2020On 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
2020NUMERICAL ANALYSIS OF THE NONLINEAR WAVE SYSTEMS BY A NOVEL ITERATIVE METHOD
YILDIRIM Ö., UZUN M.
ICFAS 2020, 06 October 2020
2020
2020On 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
2019On 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
2019Symmetry 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
2019On 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
2019A 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
2019ON 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
2019Lie 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
2019A 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
2018Invariant 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
2018NUMERICAL 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
2018On 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
2017Unique 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
2017A 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
2017On 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
2016On the analytical solution methods for sine Gordon equation
Yıldırım Ö., Uzun M.
ICAAM 2016, Almati, Kazakhstan, 7 - 10 September 2016
2016
2016On the numerical solution of sine Gordon equation
Yıldırım Ö., Uzun M.
ICAAM 2016, Almati, Kazakhstan, 7 - 10 September 2016
2016
2016On 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
2016On 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
2016On 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
2015A 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
2015On 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
2014On 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
2014On 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
2014High 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
2013ON 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
2013On 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
2012High 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
2012Stable 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
2012High 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
2011Second 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
2009A 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
2007A 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 - 2023WEAK 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 - 2023MATHEMATICAL 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 - 2022Investigation 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 - 2021ON 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 - 2020Lie 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 - 2020Applied and Computational Mathematics
Committee Member
Memberships / Tasks in Scientific Organizations
2014 - Continues
2014 - ContinuesEuropean Mathematical Society (EMS)
Member
Scientific Refereeing
June 2017
June 2017Thermal Science
SCI Journal
June 2017
June 2017Numerical Mathematics Theory Methods and Applications
SCI Journal
March 2017
March 2017FILOMAT
SCI Journal
February 2017
February 2017FILOMAT
SCI Journal
November 2016
November 2016Numerical Functional Analysis and Optimization
SCI Journal
August 2016
August 2016Springer plus
SCI Journal
July 2014
July 2014Applied Mathematics & Information Sciences
SCI Journal
Tasks In Event Organizations
Mayıs 2019
Mayıs 2019INTERNATIONAL CONFERENCE on MATHEMATICAL ADVANCES and APPLICATIONS (ICOMAA2018)
Scientific Congress
Yıldırım Ö.
İstanbul, Turkey
Mayıs 2019
Mayıs 2019INTERNATIONAL CONFERENCE on MATHEMATICAL ADVANCES and APPLICATIONS (ICOMAA2019)
Scientific Congress
Yıldırım Ö.
İstanbul, Turkey
Eylül 2018
Eylül 2018International Conference on Analysis and Applied Mathematics (ICAAM 2018)
Scientific Congress
Yıldırım Ö.
Lefkoşa, Cyprus (Kktc)
Eylül 2016
Eylül 2016International Conference on Analysis and Applied Mathematics (ICAAM 2016)
Scientific Congress
Yıldırım Ö.
Almati, Kazakhstan
Ağustos 2016
Ağustos 2016International Congress on Fundamental and Applied Sciences (ICFAS 2016)
Scientific Congress
Yıldırım Ö.
İstanbul, Turkey
Haziran 2015
Haziran 2015INTERNATIONAL CONFERENCE ON APPLIED ANALYSIS AND MATHEMATICAL MODELING (ICAAMM 2015)
Scientific Congress
Yıldırım Ö.
İstanbul, Turkey
Eylül 2014
Eylül 2014