The superconvergence of the composite trapezoidal rule for Hadamard finite part integrals (Q2581001)
From MaRDI portal
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The superconvergence of the composite trapezoidal rule for Hadamard finite part integrals |
scientific article |
Statements
The superconvergence of the composite trapezoidal rule for Hadamard finite part integrals (English)
0 references
10 January 2006
0 references
Several papers have dealt with quadrature formulas for evaluating Hadamard finite part integrals (or hypersingular integrals) with \((p+1)\)-order singularity. On the other hand the composite trapezoidal method has been applied for numerical integration and numerical solution of integral equations with smooth or weakly singular kernels. The paper deals with the superconvergence of the composite trapezoidal rule for a Hadamard finite part integral for \(p=1\) and \(p=2\). The superconvergence estimates at some special points and uniqueness of the superconvergence points are proved. Numerical results are reported for some examples to confirm the theoretical analysis. The method can be extended to integral and integro-differential equations.
0 references
Hadamard finite part integral
0 references
hypersingular integral
0 references
composite trapezoidal rule
0 references
integral equations
0 references
weakly singular kernels
0 references
superconvergence
0 references
numerical results
0 references
integro-differential equations
0 references
0 references
0 references
0 references
0 references
