A Numerical Solution of Heat Equation for Several Thermal Diffusivity Using Finite Difference Scheme with Stability Conditions

Unconditionally Stable Difference Scheme for the Numerical Solution of Nonlinear Rosenau-KdV Equation

In this paper we investigate a nonlinear evolution model described by the Rosenau-KdV equation. We propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of O(τ2 + h2). Furthermore we show the existence and uniqueness of numerical solutions. Comparing the numerical results with other methods in...

The Numerical Solution of Klein-Gorden Equation by Using Nonstandard Finite Difference

‎In this paper we propose a numerical scheme to solve the one dimensional nonlinear Klein-Gorden equation‎. ‎We describe the mathematical formulation procedure in details‎. ‎The scheme is three level explicit and based on nonstandard finite difference‎. ‎It has nonlinear denominator function of the step sizes‎. ‎Stability analysis of the method has been given and we prove that the proposed meth...

On the stability of a weighted finite difference scheme for wave equation with nonlocal boundary conditions ̊

Nonlocal problems is a major research area in many branches of modern physics, biotechnology, chemistry and engineering, which arises when it is impossible to determine the boundary values of unknown function and its derivatives. Increasingly often, there arise problems with nonlocal integral boundary conditions, especially in particle diffusion [1] and heat conduction [2, 3]. Partial different...

A Finite Difference Scheme for the Heat Conduction Equation

We use equations similar to the heat conduction equation to calulate heat transfer, radiation transfer and hydrostatical equilibrium in our stellar evolution programs. We tried various numerical schemes and found that the most convenient scheme for complicated calculations (nonlinear, multidimensional calculations) is a symmetrical semi-implicit (SSI) scheme. The (SSI) scheme is easy to code, v...

Numerical Solution of Parabolized Stability Equations Using Super Compact Scheme