The Fredholm–Volterra integral equation of the second kind with continuous kernels with respect to position and time, is solved numerically, using the Collocation and Galerkin methods. Also the error, in each case, is estimated.

The electrostatic problem of a hollow, conducting tube of finite length held at a fixed potential is solved using two methods. A twoterm Galerkin solution is constructed for the surface distribution of induced charge. The sum of a uniform component and a simple edgecondition term provides a variational solution to the dual integral equations that are the equations-of-motion for the mixed bounda...

This paper presents an efficient meshless approach for solving electrostatic problems. This novel approach is based on combination of radial basis functions-based meshless unsymmetric collocation method with projection domain decomposition method. Under this new method, we just need to solve a Steklov-Poincaré interface equation and the original problem is solved by computing a series of indepe...

The present paper develops a theory of Natural Continuous Extensions (NCEs) for the discrete approximate solution of an ODE given by a Runge-Kutta process. These NCEs are defined in such a way that the continuous solutions furnished by the one-step collocation methods are included.

Three kinds of fragile points methods based on Petrov-Galerkin weak-forms (PG-FPMs) are proposed for analyzing heat conduction problems in nonhomogeneous anisotropic media. This is a follow-up the previous study original FPM symmetric Galerkin weak-form. The trial function piecewise-continuous, written as local Taylor expansions at points. A modified radial basis function-based differential qua...

This paper is concerned with the numerical solution of implicit neutral functional diierential equations. Based on the continuous Runge{Kutta method (for ordinary diierential equations) and the collocation method (for functional equations), two general one-step methods are formulated and their uniform order of approximation are discussed. Numerical stability of a class of Runge{Kutta-Collocatio...

In this paper, we solve higher index differential algebraic equations (DAEs) by transforming them into integral algebraic equations (IAEs). We apply collocation methods on continuous piece-wise polynomials space to solve the obtained higher index IAEs. The efficiency of the given method is improved by using a recursive formula for computing the integral part. Finally, we apply the obtained algo...

in the present article, a numerical method is proposed for the numerical solution of thekdv equation by using a new approach by combining cubic b-spline functions. in this paper we convert the kdv equation to system of two equations. the method is shown to be unconditionally stable using von-neumann technique. to test accuracy the error norms2l, ∞l are computed. three invariants of motion are p...