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Zbl 1189.65306
Babolian, E.; Masouri, Z.; Hatamzadeh-Varmazyar, S.
Numerical solution of nonlinear Volterra-Fredholm integro-differential equations via direct method using triangular functions. (English)
[J] Comput. Math. Appl. 58, No. 2, 239-247 (2009). ISSN 0898-1221

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 2000:: *65R20 Integral equations (numerical methods)
45J05 Integro-ordinary differential equations
34K28 Numerical approximation of solutions of FDE
45B05 Fredholm integral equations
45D05 Volterra integral equations
65L05 Initial value problems for ODE (numerical methods)

Keywords: nonlinear integro-differential equations; direct method; vector forms; triangular functions; operational matrix

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Zentralblatt MATH Berlin [Germany]