Chebyshev methods for two dimensional parabolic equations.
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Chebyshev methods for two dimensional parabolic equations.

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Published in Bradford .
Written in English


Book details:

Edition Notes

Ph.D.thesis. Typescript.

SeriesTheses
The Physical Object
Pagination299p.
Number of Pages299
ID Numbers
Open LibraryOL13655191M

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  Chebyshev methods for the numerical solution of parabolic partial differential equations in a region which can be transformed to either a square or a circular cylinder are developed. These procedures are an extension of the method of Knibb & Scraton ().Cited by: 8. Chebyshev collocation method is successfully used for solving parabolic partial integrodifferential equation. This method reduced the considered problem into linear system of algebraic equations that can be solved successively to obtain a numerical solution at varied time by: 6.   We provide a new effective method for the two-dimensional distributed-order fractional differential equations (DOFDEs). The technique is based on fractional-order Chebyshev wavelets. An exact formula involving regularized beta functions for determining the Riemann-Liouville fractional integral operator of these wavelets is given. In this paper, the Chebyshev Gauss-Lobatto pseudospectral scheme is investigated in spatial directions for solving one-dimensional, coupled, and two-dimensional parabolic partial differential equations with time delays. For the one-dimensional problem, the spatial integration is discretized by the Chebyshev pseudospectral scheme with Gauss-Lobatto quadrature nodes to provide a delay system .

In this paper, a new family of fourth order Chebyshev methods (also called stabilized methods) is constructed. These methods possess nearly optimal stability regions along the negative real axis and a three-term recurrence relation. The stability properties and the high order make them suitable for large stiff problems, often space discretization of parabolic PDEs. Parabolic Equations of Higher than the Second Order Non-linear Equations Conclusions Part II. Solution of Net Equations Introduction 1. "One-dimensional" Elliptic Net Equations 2. Direct Methods 3. Ill-conditioned Net Matrices 4. Simplest Iterative Method 5. Variational Methods 6. Methods using Chebyshev Polynomials 7. Iterative Methods. equation is almost an important topic in recent years. In this paper, in order to solve the numerical solution of a class of fractional partial differential equation of parabolic type, we present a collocation method of two-dimensional Chebyshev wavelets. Using the definition and property of Chebyshev.   [4] M. Heigemann, Chebyshev matrix operator method for the solution of integrated forms of linear ordinary differential equations, Acta Mech (to appear). [5] W. Huang and D.M. Sloan, The pseudospectral method for solving differential eigenvalue problems,J. Comput. Phys. , .

In this paper, we use a time splitting method with higher-order accuracy for the solutions (in space variables) of a class of two-dimensional semi-linear parabolic equations. Galerkin-Chebyshev pseudo spectral method is used for discretization of the spatial derivatives, and implicit Euler method is used for temporal discretization.   method requires that the lower boundary be perfectly free, and the calcula-tion speed is slow. We have presented normal mode and standard parabolic equation models using the Chebyshev-Tau spectral method to process a sin-gle layer of a body of . To this end, we present a Chebyshev multidomain (CMD) Pseudospectral method to solve a simple two variable cardiac models on three-dimensional anisotropic media and we show the usefulness of the method over the traditional finite differences scheme widely used in the literature. In this paper, we present a high-order accurate method for two-dimensional semilinear parabolic equations. The method is based on a Galerkin-Chebyshev spectral method for discretizing spatial derivatives and a block boundary value methods of fourth-order for temporal discretization. Our formulation has high-order accurate in both space and time.