Polynomial and nonpolynomial spline methods for fractional sub-diffusion equations |
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Authors: | S Mohammad Hosseini Rezvan Ghaffari |
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Institution: | Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-175, Tehran, Iran |
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Abstract: | We consider one-dimensional fractional sub-diffusion equations on an unbounded domain. For a problem of this type for which an exact or approximate artificial boundary condition is available we reduce it to an initial-boundary value problem on a bounded domain. We then analyze the numerical solution of the problem by polynomial and nonpolynomial spline methods. The consistency and the Von Neumann stability analysis of these methods are also discussed. Numerical experiments clarify the effectiveness and order of accuracy of the proposed methods. |
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Keywords: | Fractional differential equation Quadratic spline Cubic polynomial spline Nonpolynomial spline Stability |
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