Abstract
Recently many research works have been conducted and published regarding fractional order differential equations. There are several approaches available for numerical approximations of the solution of fractional order diffusion equations. Spectral collocation method based on Lagrange’s basis polynomials to approximate numerical solutions of one-dimensional (1D) space fractional diffusion equations are introduced in this research paper. The proposed form of approximate solution satisfies non-zero Dirichlet’s boundary conditions on both boundaries. Collocation scheme produce a system of first order Ordinary Differential Equations (ODE) from the fractional diffusion equation. We applied this method with four different sets of collocation points to compare their performance.
Highlights
In recent times, a huge number of research articles have been published by researchers around the world regarding development of various methods for fractional differential equations
Collocation scheme produce a system of first order Ordinary Differential Equations (ODE) from the fractional diffusion equation
We will present a spectral collocation method where approximate solution will be expressed in terms of Lagrange’s basis polynomials in space and a system of first order ODE for time variable is generated by collocation scheme from space fractional diffusion equation
Summary
A huge number of research articles have been published by researchers around the world regarding development of various methods for fractional differential equations. Azizi and Loghmani [3] used Chebyshev spectral collocation method but they reduced the fractional diffusion equation into a set of algebraic equations using Chebyshev polynomials and Gauss-Lobatto nodes in both space and time domain. They discussed spectral collocation method based on Lagrange’s basis polynomials and Gauss-Lobatto nodes With these methods they solve space fractional diffusion equation that have Dirichlet’s boundary conditions; zero in one boundary and non-zero in another. We will present a spectral collocation method where approximate solution will be expressed in terms of Lagrange’s basis polynomials in space and a system of first order ODE for time variable is generated by collocation scheme from space fractional diffusion equation.
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