First Order Multistep Method for Solving Diffusion Convection Equations Derivable from Polynomials as Basis Functions and its Applications.

In this work, a new numerical finite difference scheme for the solution of heat diffusion conduction equation arising from heat conduction is developed due to the recent growing interest in literatures in the derivation of continuous numerical finite difference method for solving heat diffusion convection equations. This was done based on the collocation and interpolation of the heat diffusion convection equations directly over multi steps along lines but without reduction to a system of Ordinary Differential Equations (ODE). The intention was to avoid the cost of solving a large system of coupled ODEs often arising from the reduction method by a semi - discretization. The performance of the new numerical finite difference scheme was tested. The numerical results obtained showed that the method provided the same results with the known explicit finite difference method. There was no semi-discretization involved in the derivation of this scheme, and no reduction of the heat diffusion convection equations to a system of ODE is recorded, but rather a system of algebraic equations is formulated. Therefore, the desire is to derive a new numerical scheme that will be used in finding the solutions of the system of algebraic equations formulated from the discretization of the heat diffusion convection equations with respect to the space and time variables. This new numerical method was applied to solve two different test problems with known explicit solutions by Schmidt. [ABSTRACT FROM AUTHOR]