Solution of nonlinear Volterra-Fredholm integrodifferential equations via hybrid of block-pulse functions and Lagrange interpolating polynomials. (English) Zbl 1268.65168
Summary: An efficient hybrid method is developed to approximate the solution of the high-order nonlinear Volterra-Fredholm integro-differential equations. The properties of hybrid functions consisting of block-pulse functions and Lagrange interpolating polynomials are first presented. These properties are then used to reduce the solution of the nonlinear Volterra-Fredholm integro-differential equations to the solution of algebraic equations whose solution is much more easier than the original one. The validity and applicability of the proposed method are demonstrated through illustrative examples. The method is simple, easy to implement and yields very accurate results.
MSC:
| 65R20 | Numerical methods for integral equations |
| 45J05 | Integro-ordinary differential equations |
| 45B05 | Fredholm integral equations |
| 45D05 | Volterra integral equations |
| 45G10 | Other nonlinear integral equations |
Keywords:
numerical examples; high-order nonlinear Volterra-Fredholm integro-differential equations; block-pulse functions; Lagrange interpolating polynomialsReferences:
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