A new numerical method for solving two-dimensional Volterra-Fredholm integral equations. (English) Zbl 1354.65278
The authors present a new numerical method for solving two-dimensional Volterra-Fredholm integral equations. A review of block pulse functions (BPFs) and triangular functions (TFs) is briefly given. One-dimensional delta functions (1D-DFs), 2-dimensional delta functions (2D-DFs) descriptions and properties are given. How to use 2D-DFs to reduce the Volterra-Fredholm integral equations to a system of nonlinear algebraic equations is explained. Convergence analysis is given and numerical examples are given to illustrate the efficiency and accuracy of the algorithms discussed.
Reviewer: Seenith Sivasundaram (Daytona Beach)
MSC:
| 65R20 | Numerical methods for integral equations |
| 45B05 | Fredholm integral equations |
| 45D05 | Volterra integral equations |
| 45G10 | Other nonlinear integral equations |
Keywords:
two-dimensional Volterra-Fredholm integral equations; delta functions; operational matrix; vector forms; error analysis; block pulse functions; convergence; numerical examples; algorithmReferences:
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