Projected iterations of fixed-point type to solve nonlinear partial Volterra integro-differential equations. (English) Zbl 1474.45018
Summary: In this paper, we propose a method to approximate the fixed point of an operator in a Banach space. Using biorthogonal systems, this method is applied to build an approximation of the solution of a class of nonlinear partial integro-differential equations. The theoretical findings are illustrated with several numerical examples, confirming the reliability, validity and precision of the proposed method.
MSC:
| 45D05 | Volterra integral equations |
| 45L05 | Theoretical approximation of solutions to integral equations |
| 45N05 | Abstract integral equations, integral equations in abstract spaces |
| 47H10 | Fixed-point theorems |
| 47N20 | Applications of operator theory to differential and integral equations |
| 65R20 | Numerical methods for integral equations |
Keywords:
operators in Banach spaces; fixed-point theorem; biorthogonal systems; numerical methods; nonlinear partial integro-differential equationsReferences:
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