Numerical solution of the system of nonlinear Fredholm integro-differential equations by the operational tau method with an error estimation. (English) Zbl 1178.65146

Summary: The operational approach to the Tau method is used for the numerical solution of a nonlinear Fredholm integro-differential equations and nonlinear ordinery differential equaions with initial or boundary conditions without linearizing. An efficient error estimation of the approximate solution is also introduced. Some examples are given to clarify the efficiency and high accuracy of the method.


65R20 Numerical methods for integral equations
45G15 Systems of nonlinear integral equations
45B05 Fredholm integral equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
45J05 Integro-ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems