On multi-singular integral equations involving n weakly singular kernels

A Hybrid Collocation Method for Volterra Integral Equations with Weakly Singular Kernels

The commonly used graded piecewise polynomial collocation method for weakly singular Volterra integral equations may cause serious round-off error problems due to its use of extremely nonuniform partitions and the sensitivity of such time-dependent equations to round-off errors. The singularity preserving (nonpolynomial) collocation method is known to have only local convergence. To overcome th...

The semi-explicit Volterra integral algebraic equations with weakly singular kernels: The numerical treatments

Product integration for Volterra integral equations of the second kind with weakly singular kernels

We introduce a new numerical approach for solving Volterra integral equations of the second kind when the kernel contains a mild singularity. We give a convergence result. We also present numerical examples which show the performance and efficiency of our method.

CAS WAVELET METHOD FOR THE NUMERICAL SOLUTION OF BOUNDARY INTEGRAL EQUATIONS WITH LOGARITHMIC SINGULAR KERNELS

In this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the Laplacian equation. Themethod is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis.This approach utilizes the non-uniform Gauss-Legendre quadrature rule for ...

A Nyström-like Approach to Integral Equations with Singular Kernels

Traditional boundary element methods use panel-based discretization and exhibit low order convergence. In this paper, a new approach is proposed to discretize a singular integral equation. Global, numerically orthogonal bases are used to represent a solution, and mapping functions are used to represent the geometry. This method is capable of achieving spectral convergence, similar to the Nyströ...