ON SOLUTIONS OF LINEAR FUNCTIONAL INTEGRAL AND INTEGRO-DIFFERENTIAL EQUATIONS VIA LAGRANGE POLYNOMIALS

YÜZBAŞI Ş., SEZER M.

Journal of Science and Arts, vol.21, 2021 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 21
  • Publication Date: 2021
  • Doi Number: 10.46939/j.sci.arts-21.3-a11
  • Journal Name: Journal of Science and Arts
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Keywords: Interpolation and collocation points, Lagrange polynomials, Lagrange collocation method, residual error, residual function, COLLOCATION METHOD, NUMERICAL-SOLUTION, DIFFERENCE-EQUATIONS, RESIDUAL CORRECTION, MATRIX-METHOD, SYSTEMS, APPROXIMATIONS, ALGORITHM
  • Akdeniz University Affiliated: Yes

Abstract

In this study, a matrix-collocation method is developed numerically to solve the linear Fredholm-Volterra-type functional integral and integro-differential equations. The linear functional integro-differential equations are considered under initial conditions. The mentioned type problems often appear in various branches of science and engineering such as physics, biology, mechanics, electronics. The method essentially is a collocation method based on the Lagrange polynomials and matrix operations. By using presented method, the problem is reduced to a system of linear algebraic equations. The solution of this system gives the coefficients of assumed solution. An error analysis based on the residual function is studied. Some examples are solved to demonstrate the accuracy and efficiency of the method.