Collocation Methods for Hyperbolic Partial Differential Equations with Singular Sources
نویسندگان
چکیده
منابع مشابه
Numerical studies of non-local hyperbolic partial differential equations using collocation methods
The non-local hyperbolic partial differential equations have many applications in sciences and engineering. A collocation finite element approach based on exponential cubic B-spline and quintic B-spline are presented for the numerical solution of the wave equation subject to nonlocal boundary condition. Von Neumann stability analysis is used to analyze the proposed methods. The efficiency, accu...
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An integration algorithm that conjugates a Method of Lines (MOL) strategy based on finite differences space discretizations, with a collocation strategy based on increasing level dyadic grids is presented. It reveals potential either as a grid generation procedure and a Partial Differential Equation (PDE) integration scheme. It copes satisfactorily with a example characterized by a steep travel...
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متن کاملSpectral Collocation Methods for a Partial Integro-differential Equation with a Weakly Singular Kernel
We propose and analyze the spectral collocation approximation for the partial integrodifferential equations with a weakly singular kernel. The space discretization is based on the pseudo-spectral method, which is a collocation method at the Gauss-Lobatto quadrature points. We prove unconditional stability and obtain the optimal error bounds which depend on the time step, the degree of polynomia...
متن کاملA note on collocation methods for Volterra integro-differential equations with weakly singular kernels
will be employed in the analysis of the principle properties of the collocation approximations; the extension to nonlinear equations is straightforward (cf. [1, p. 225]). High-order numerical methods for VIDEs with weakly singular kernels may be found in [1,2,6,7,8]. In this note we shall consider collocation methods for VIDE (1.1), based on Brunner's approach [1]. The following method and nota...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics and Mechanics
سال: 2009
ISSN: 2070-0733,2075-1354
DOI: 10.4208/aamm.09-m09s10