A Numerical Method for Solving Second-Order Linear Partial Differential Equations Under Dirichlet, Neumann and Robin Boundary Conditions

YÜZBAŞI Ş.

INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS, cilt.14, sa.2, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 2
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1142/s0219876217500153
  • Dergi Adı: INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Partial differential equations, bessel functions of first kind, bessel collocation method, collocation points, numerical solutions, residual function, residual correction, COLLOCATION METHOD, HOMOTOPY PERTURBATION, GALERKIN METHOD, SIMULATION, APPROXIMATION, INTERPOLATION, SYSTEM, FORM
  • Akdeniz Üniversitesi Adresli: Evet

Özet

The aim of this paper is to give a collocation method to solve second-order partial differential equations with variable coefficients under Dirichlet, Neumann and Robin boundary conditions. By using the Bessel functions of the first kind, the matrix operations and the collocation points, the method is constructed and it transforms the partial differential equation problem into a system of algebraic equations. The unknown coefficients of the assuming solution are determined by solving this system. The algorithm of the proposed method is presented. Also, error estimation technique is introduced and the approximate solutions are improved by means of it. To show the validity and applicability of the presented method, we solve numerical examples and give the comparison of solutions and comparisons of the errors (actual and estimation).