Discrete Maximum Principle in One-Dimensional Heat Equation

NUMERICAL SOLUTION OF ONE-DIMENSIONAL HEAT AND WAVE EQUATION BY NON-POLYNOMIAL QUINTIC SPLINE

This paper present a novel numerical algorithm for the linear one-dimensional heat and wave equation. In this method, a nite dierenceapproach had been used to discrete the time derivative while cubic spline isapplied as an interpolation function in the space dimension. We discuss theaccuracy of the method by expanding the equation based on Taylor series andminimize the error. The proposed metho...

A Galerkin B-spline Approach to One Dimensional Heat Equation

In this paper a numerical solution of one dimensional heat equation is presented using Galerkin B-spline finite element method. Quadratic B-spline basis functions are used for finding the solution. Two test problems are studied to evaluate the efficiency of the given technique. Numerical algorithms are developed for the simulation to hold. Results obtained are compared with the exact solution a...

A Weak Discrete Maximum Principle and Stability

Let ÍÍ be a polygonal domain in the plane and Sy(£l) denote the finite element space of continuous piecewise polynomials of degree < r — 1 (r > 2) defined on a quasi-uniform triangulation of ii (with triangles roughly of size h). It is shown that if un e Sy(Sl) is a "discrete harmonic function" then an a priori estimate (a weak maximum principle) of the form ""ftHi^n) < CII"/illL„.(3iï) holds. ...

Extensions of the Maximum Principle: Exponential Preservation by the Heat Equation

Numerical solution for one-dimensional independent of time Schrödinger Equation

In this paper, one of the numerical solution method of one- particle, one dimensional timeindependentSchrodinger equation are presented that allows one to obtain accurate bound state eigenvalues and functions for an arbitrary potential energy function V(x).For each case, we draw eigen functions versus the related reduced variable for the correspondingenergies. The paper ended with a comparison ...