Solution of Second Order Ordinary Differential Equation Associated with Toeplitz and Stiffness Matrices

Abstract

In this work we develop a technique solution of second order ordinary differential equation (integrating by parts) to reach to Toeplitz matrices and Stiffness matrix to solve O.D.Es. We investigate that solution numerically using finite difference method and we find the error between exact and numerical solution computed using finite element.

Solution of Laplace’s Equation in A Singular Domain Using Mellin Transform

“…In fact in the choice of the conditions of interface one must take into account the nature of the corners [5,8,9,1,2]. We will show that for corners inside the complete domain or corners on the edge of the complete domain with Neumann condition on the edge, the conditions of connection to the interfaces must not contain a constant term to have a well-posed problem which allows non-zero values at the corner.…”

A Comparison of Different Numerical Schemes to Solve Nonlinear First Order ODE

“…Euler method (also called forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge-Kutta method [1] [2] [3]. The backward Euler method (or implicit Euler method) is one of the most basic numerical methods for the solution of ordinary differential equations, the backward Euler method has order one.…”