NUMERICAL SOLUTIONS FOR SPACE FRACTIONAL DISPERSION EQUATIONS WITH NONLINEAR SOURCE TERMS
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초록
Numerical solutions for the fractional differential dispersion equations with nonlinear forcing terms are considered. The backward Euler finite difference scheme is applied in order to obtain numerical so-lutions for the equation. Existence and stability of the approximate solu-tions are carried out by using the right shifted Grünwald formula for the fractional derivative term in the spatial direction. Error estimate of order O(Δx + Δt) is obtained in the discrete L2 norm. The method is applied to a linear fractional dispersion equations in order to see the theoretical order of convergence. Numerical results for a nonlinear problem show that the numerical solution approach the solution of classical diffusion equation as fractional order approaches 2.
Abstract
Numerical solutions for the fractional differential dispersion equations with nonlinear forcing terms are considered. The backward Euler finite difference scheme is applied in order to obtain numerical so-lutions for the equation. Existence and stability of the approximate solu-tions are carried out by using the right shifted Grünwald formula for the fractional derivative term in the spatial direction. Error estimate of order O(Δx + Δt) is obtained in the discrete L2 norm. The method is applied to a linear fractional dispersion equations in order to see the theoretical order of convergence. Numerical results for a nonlinear problem show that the numerical solution approach the solution of classical diffusion equation as fractional order approaches 2.
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