Computer Oriented Numerical Scheme for Solving Engineering Problems

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Shams M., Rafiq N., Kausar N., Mir N. A., Alalyani A.

COMPUTER SYSTEMS SCIENCE AND ENGINEERING, cilt.42, sa.2, ss.689-701, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 2
  • Basım Tarihi: 2022
  • Doi Numarası: 10.32604/csse.2022.022269
  • Dergi Adı: COMPUTER SYSTEMS SCIENCE AND ENGINEERING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, PASCAL, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.689-701
  • Anahtar Kelimeler: Biomedical engineering, convergence order, iterative method, CPU-time, simultaneous method, NONLINEAR EQUATIONS, ITERATIVE METHODS, ORDER, ZEROS
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In this study, we construct a family of single root finding method of optimal order four and then generalize this family for estimating of all roots of non-linear equation simultaneously. Convergence analysis proves that the local order of convergence is four in case of single root finding iterative method and six for simultaneous determination of all roots of non-linear equation. Some non-linear equations are taken from physics, chemistry and engineering to present the performance and efficiency of the newly constructed method. Some real world applications are taken from fluid mechanics, i.e., fluid permeability in biogels and biomedical engineering which includes blood Rheology-Model which as an intermediate result give some nonlinear equations. These non-linear equations are then solved using newly developed simultaneous iterative schemes. Newly developed simultaneous iterative schemes reach to exact values on initial guessed values within given tolerance, using very less number of function evaluations in each step. Local convergence order of single root finding method is computed using CAS-Maple. Local computational order of convergence, CPU-time, absolute residuals errors are calculated to elaborate the efficiency, robustness and authentication of the iterative simultaneous method in its domain.