Introduction to Multi Term Time Space
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In this paper, we present an efficient alternating direction implicit (ADI) scheme for two-dimensional multi-term time-space fractional nonlinear diffusion-wave equations.
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Firstly, the equation is transformed into a multi-term time-space fractional wave equation using the mid-point quadrature rule to approximate the distributed-order Riesz space derivative.
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We propose the following two new computational multi-term time-space fractional diffusion models in three dimensions, which can be used to simulate multi-term time-space fractional Bloch-Torrey models in three dimensions: Model I: Finite element method for the multi-term time-space fractional diffusion model with Riesz fractional operator; Model II: Finite difference method for the multi-term time-space fractional diffusion equation with fractional Laplacian operator.
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In this study, the Ritz–Galerkin method based on Legendre multiwavelet functions is introduced to solve multi-term time-space convection–diffusion equations of fractional order with variable coefficients and initial-boundary conditions.
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