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Compact finite difference method for integro-differential equations. (English) Zbl 1102.65144
The paper is concerned with developing a method for the approximate solution of (Fredholm) integro-differential equations. The authors remark that the method proposed can also be applied to Volterra equations. The starting point is a compact finite difference scheme for the second order derivatives. After a brief review of the sixth order scheme the authors explain how the approach can be adapted for integro-differential equations, and how the boundary conditions are used. Various theorems on errors are derived and numerical examples are given. The main conclusion of the paper is that the resulting numerical scheme gives fifth order accuracy for integro-differential equations.
MSC:
65R20Integral equations (numerical methods)
45J05Integro-ordinary differential equations