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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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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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참고문헌 (13)
참고문헌 신청
B. Baeumer / 2007 / Fractional reproduction-dispersal equa-tions and heavy tail dispersal kernels / Bull. Math. Biol. 69 (7) : 2281 ~ 2297
B. Baeumer / 2008 / Numerical solutions for fractional reaction-diffusion equations / Comput. Math. Appl. 55 (10) : 2212 ~ 2226
C. Tadjeran / 2006 / A second-order accurate numerical approximation for the fractional diffusion equation / J. Comput. Phys. 213 (1) : 205 ~ 213
H. Ye / 2007 / A generalized Gronwall inequality and its application to a fractional differential equation / J. Math. Anal. Appl. 328 (2) : 1075 ~ 1081
J. M. Ortega / 1970 / Iterative Solution of Nonlinear Equations in Several Variables / Academic Press
B. Baeumer / 2008 / Numerical solutions for fractional reaction-diffusion equations / Comput. Math. Appl. 55 (10) : 2212 ~ 2226
C. Tadjeran / 2006 / A second-order accurate numerical approximation for the fractional diffusion equation / J. Comput. Phys. 213 (1) : 205 ~ 213
H. Ye / 2007 / A generalized Gronwall inequality and its application to a fractional differential equation / J. Math. Anal. Appl. 328 (2) : 1075 ~ 1081
J. M. Ortega / 1970 / Iterative Solution of Nonlinear Equations in Several Variables / Academic Press
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