A compatible Hermite–Taylor matrix-collocation technique with convergence test for second-order partial integro-differential equations containing two independent variables with functional bounds

Abstract

The aim of this study is to offer a compatible numerical technique to solve second-order linear partial integro-differential equations with variable (functional) bounds, including two independent variables, under the initial and/or boundary conditions by using hybrid Hermite and Taylor series. The method converts the presented integro-differential equation to a matrix equation including the unknown Hermite coefficients. Solving this matrix equation and applying the collocation method, the approximate solution of the problem is obtained in terms of the Hermite polynomials. Also, by means of an error estimation and convergence test related to residual functions, some examples to illustrate the accuracy and efficiency of the method are fulfilled; the obtained results are scrutinized and interpreted. All numerical computations have been performed on the computer programs.

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Yalçın, E., Sezer, M. A compatible Hermite–Taylor matrix-collocation technique with convergence test for second-order partial integro-differential equations containing two independent variables with functional bounds. Math Sci (2021). https://doi.org/10.1007/s40096-021-00393-6

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Keywords

  • Hermite and Taylor polynomials
  • Partial integro-differential equations
  • Matrix-collocation method
  • Variable bounds
  • Residual error analysis