Laplace Transform Collocation Method for Solving Hyperbolic Telegraph Equation

A Numerical Method for Solving the Hyperbolic Telegraph Equation

Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this article, we propose a numerical scheme to solve the one-dimensional hyperbolic telegraph equation using collocation points and approximating the solution using thin plate splines radial basis function. The scheme works in a simila...

The variational iteration method for solving Nagumo telegraph equation

Numerical solution of second order one dimensional hyperbolic telegraph equation by cubic B-spline collocation method

The present paper uses new approach and methodology to solve second order one dimensional hyperbolic telegraph equation numerically by B-spline collocation method. It is based on collocation of modified cubic B-spline basis functions over the finite elements. The given equation is decomposed into system of equations and modified cubic B-spline basis functions have been used for spatial variable...

The Laplace transform method for Burgers’ equation

The Laplace transform method (LTM) is introduced to solve Burgers’ equation. Because of the nonlinear term in Burgers’ equation, one cannot directly apply the LTM. Increment linearization technique is introduced to deal with the situation. This is a key idea in this paper. The increment linearization technique is the following: In time level t , we divide the solution u(x, t) into two parts: u(...

Solving the Laplace equation by meshless collocation using harmonic kernels

We present a meshless technique which can be seen as an alternative to the Method of Fundamental Solutions (MFS). It calculates homogeneous solutions of the Laplacian (i.e. harmonic functions) for given boundary data by a direct collocation technique on the boundary using kernels which are harmonic in two variables. In contrast to the MFS, there is no artifical boundary needed, and there is a f...