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RISAn Efficient Legendre Spectral Tau Matrix Formulation for Solving Fractional Subdiffusion and Reaction Subdiffusion Equations
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: In this work, we discuss an operational matrix approach for introducing an approximate solution of the fractional subdiffusion equation (FSDE) with both Dirichlet boundary conditions (DBCs) and Neumann boundary conditions ...
An Accurate Jacobi Pseudospectral Algorithm for Parabolic Partial Differential Equations With Nonlocal Boundary Conditions
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: A new spectral Jacobi–Gauss–Lobatto collocation (J–GL–C) method is developed and analyzed to solve numerically parabolic partial differential equations (PPDEs) subject to initial and nonlocal boundary conditions. ...
On Generalized Jacobi–Bernstein Basis Transformation: Application of Multidegree Reduction of Bأ©zier Curves and Surfaces
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: This paper formulates a new explicit expression for the generalized Jacobi polynomials (GJPs) in terms of Bernstein basis. We also establish and prove the basis transformation between the GJPs basis and Bernstein basis and ...
A Spectral Numerical Method for Solving Distributed-Order Fractional Initial Value Problems
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: In this paper, we construct and analyze a Legendre spectral-collocation method for the numerical solution of distributed-order fractional initial value problems. We first introduce three-term recurrence relations for the ...
An Efficient Operational Matrix Technique for Multidimensional Variable Order Time Fractional Diffusion Equations
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: This paper derives a new operational matrix of the variableorder (VO) time fractional partial derivative involved in anomalous diffusion for shifted Chebyshev polynomials. We then develop an accurate numerical algorithm ...