A modified non-linear transformation method for evaluating weakly singular boundary integrals

An adaptive element subdivision technique for evaluating 3D weakly singular boundary integrals

A general adaptive element subdivision technique is presented for the numerical evaluation of weakly singular integrals, which often appear in three-dimensional boundary element analysis equations. In this algorithm, the weakly singular boundary element is broken up into a few sub-elements through a sphere of decreasing radius. The sub-elements involving the singular point are evaluated numeric...

A Method to Estimate the Solution of a Weakly Singular Non-linear Integro-differential Equations by Applying the Homotopy Methods

A General New Algorithm for Regulaization of Singular Integrals in Three-Dimensional Boundary Elemnts

In this paper an algorithm is presented for the regularization of singular integrals with any degrees of singularity, which may be employed in all three-dimensional problems analyzed by Boundary Elements. The integrals in Boundary Integrals Equations are inherently singular. For example, one can mention the integrals confronted in potential problems to evaluate the flow or the gradient of the f...

A new modified quadrature method for solving linear weakly singular integral equations

One kind of linear integral equation is the weakly singular integral equation; this kind of integral equation is unsolvable by using usual quadrature methods, such as the repeated trapezoid and repeated Simpson quadrature methods. In this article, we intend to present a subtraction method, which is the same as the modified quadrature methods; one can solve linear weakly singular integral equati...

Convergence of product integration method applied for numerical solution of linear weakly singular Volterra systems

We develop and apply the product integration method to a large class of linear weakly singular Volterra systems. We show that under certain sufficient conditions this method converges. Numerical implementation of the method is illustrated by a benchmark problem originated from heat conduction.