SYMPOSIUM KEYNOTE PRESENTATIONS

ABSTRACT

An efficient high order finite difference algorithm for solving systems of reaction-diffusion equations will be discussed in this presentation. The reaction term is nonlinear and the diffusion term is linear. The algorithm is unconditionally stable, second order accurate in time, and fourth order accurate in space. The computational complexity of this algorithm is similar to that of the traditional Crank-Nicholson algorithm, which is only second order accurate in space. It is more efficient than the standard high order compact finite difference algorithm since no derivatives are used as unknown dependent variables. The computational efficiency is further improved by representing the unknowns in the nonlinear reaction term using extrapolations from the solutions at previous time steps. Numerical results will be discussed in the presentation to demonstrate significant accuracy and efficiency

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