## Numerical solution of nonlinear Volterra-Fredholm integro-differential equations via direct method using triangular functions.(English)Zbl 1189.65306

Summary: An effective direct method to determine the numerical solution of the specific nonlinear Volterra-Fredholm integro-differential equations is proposed. The method is based on new vector forms for representation of triangular functions and its operational matrix. This approach needs no integration, so all calculations can be easily implemented. Some numerical examples are provided to illustrate the accuracy and computational efficiency of the method.

### MSC:

 65R20 Numerical methods for integral equations 45J05 Integro-ordinary differential equations 34K28 Numerical approximation of solutions of functional-differential equations (MSC2010) 45B05 Fredholm integral equations 45D05 Volterra integral equations 65L05 Numerical methods for initial value problems involving ordinary differential equations
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### References:

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