Modification of Laplace Adomian decomposition method for solving nonlinear Volterra integral and integro-differential equations based on Newton Raphson formula. (English) Zbl 1384.65096
Summary: In this paper, we establish a modified Laplace decomposition method for nonlinear volterra integral and integro-differential equations. This technique differs from the general Laplace decomposition method because of the terms involved in Adomian polynomial. We have used Newton Raphson formula in place of the \(u_{i}\) in Adomian polynomial. The proposed scheme is investigated with some illustrative examples and has given reliable results.
MSC:
| 65R20 | Numerical methods for integral equations |
| 45D05 | Volterra integral equations |
| 45G10 | Other nonlinear integral equations |
| 45J05 | Integro-ordinary differential equations |
Keywords:
numerical Laplace transform method; Volterra integral equations; Volterra integro-differential equations; Adomian decomposition method; Newton Raphson formula; nonlinearReferences:
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