NASA Technical Reports Server (NTRS) : A pdf

NASA Technical Reports Server (NTRS) : A

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We derive a deterministic particle method for the solution of nonlinear reaction-diffusion equations in one spatial dimension. This deterministic method is an analog of a Monte Carlo method for the solution of these problems that has been previously investigated by the author. The deterministic method leads to the consideration of a system of ordinary differential equations for the positions of suitably defined particles. We then consider the time explicit and implicit methods for this system of ordinary differential equations and we study a Picard and Newton iteration for the solution of the implicit system. Next we solve numerically this system and study the discretization error both analytically and numerically. Numerical computation shows that this deterministic method is automatically adaptive to large gradients in the solution

• Creator/s: NASA Technical Reports Server (NTRS
• Date: 11/1/1995
• Year: 1995
• Book Topics/Themes: NASA Technical Reports Server (NTRS), BOUNDARY LAYER EQUATIONS, MONTE CARLO METHOD, NONLINEAR EQUATIONS, NUMERICAL ANALYSIS, PARTICLES, TIME DISCRIMINATION, DIFFERENTIAL EQUATIONS, MEAN SQUARE VALUES, REACTION-DIFFUSION EQUATIONS, Mascagni, Michael

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