In this article, we introduce a modification of the Taylor matrix method using Pad´e approximation to obtain an accurate solution of linear system of Fredholm integro-differential equations (FIDEs). This modification is based on, first, taking truncated Taylor series of the functions and then substituting their matrix forms into the given equations. Thereby the equation reduces to a matrix equation, which corresponds to a system of linear algebraic equations with unknown Taylor coefficients. Finally, we use Pad´e approximation to obtain an accurate numerical solution of the proposed problem. To demonstrate the validity and the applicability of the proposed method, we present some numerical examples. A comparison with the standard Taylor matrix method is given.
Khader, M. M.
Application of Taylor-Pade technique for obtaining approximate solution for system of linear Fredholm integro-dierential equations,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 12,
1, Article 25.
Available at: https://digitalcommons.pvamu.edu/aam/vol12/iss1/25