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Material engineers are excited with the design of a new rubber product through the development of a new composite of the rubber product. Our research contributes in developing the mathematical simulation based on Gauss-Seidel Red-Black and Gauss-Seidel method to solve the temperature behavior of the rubber elasticity, strength, entropy and classical experiments through reference publications and stimulating rubber physics research elsewhere. The temperature behavior leads to the partial differential equation of heat transfer problems involving phase change simulation. The prototype of the algorithm implemented on Linux operating systems using C language.

This paper will discuss the solution of twodimensional partial differential equations (PDEs) using some parallel numerical methods namely Gauss Seidel and Red Black Gauss Seidel. The selected two-dimensional PDE to solve in this paper are of parabolic and elliptic type. Parallel Virtual Machine (PVM) is used in support of the communication among all microprocessors of Parallel Computing System. PVM is well known as a software system that enables a collection of heterogeneous computers to be used as coherent and flexible concurrent computational resource. The numerical results will be presented graphically and parallel performance measurement by Gauss Seidel and Red Gauss Seidel methods will be evaluated in terms of execution time, speedup, efficiency, effectiveness and temporal performance. Performance evaluations are critical as this paper aimed to fabricate an efficient Two-Dimensional PDE Solver (TDPDES). This new well-organized TDPDES technique will enhance the research and analysis procedure of many engineering and mathematic fields.

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