A collocation method for solving some integral equations in distributions. (English) Zbl 1232.65183
The paper is concerned with the numerical solution, using a collocation method, or integral equations of class \(\mathcal{R}\), whose kernels are positive rational functions of arbitrary selfadjoint elliptic operators.
Following background and basic definitions, the authors describe the collocation method and give conditions under which the resulting linear system is uniquely solvable. Some basic convergence results are given. The choice of basis functions is discussed and the paper concludes with numerical experiments that demonstrate the effectiveness of the approach.
Following background and basic definitions, the authors describe the collocation method and give conditions under which the resulting linear system is uniquely solvable. Some basic convergence results are given. The choice of basis functions is discussed and the paper concludes with numerical experiments that demonstrate the effectiveness of the approach.
Reviewer: Neville Ford (Chester)
MSC:
| 65R20 | Numerical methods for integral equations |
| 45A05 | Linear integral equations |
| 45P05 | Integral operators |
| 46F05 | Topological linear spaces of test functions, distributions and ultradistributions |
| 46F10 | Operations with distributions and generalized functions |
Keywords:
integral equations in distributions; signal estimation; collocation method; convergence; numerical experimentsReferences:
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