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

YÜZBAŞI Ş., SEZER M.

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

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 21
  • Basım Tarihi: 2021
  • Doi Numarası: 10.46939/j.sci.arts-21.3-a11
  • Dergi Adı: Journal of Science and Arts
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Anahtar Kelimeler: 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 Üniversitesi Adresli: Evet

Özet

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.