A spline-in-compression method, implicit in nature, for computing numerical solution of second order nonlinear initial-value problems (IVPs) on a mesh not necessarily equidistant is discussed. The proposed estimation ...
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A spline-in-compression method, implicit in nature, for computing numerical solution of second order nonlinear initial-value problems (IVPs) on a mesh not necessarily equidistant is discussed. The proposed estimation has been derived directly from consistency condition which is third-order accurate. For scientific computation, we use monotonically descending step lengths. The suggested method is applicable to a wider range of physical problems including the problems which are singular in nature. This is possible due to off-step discretization employed in the spline technique. We examine the absolute stability and super-stability of the method when applied to a problem of physical significances. We have shown that the method is absolutely stable in the case of graded mesh and super stable in the case of constant mesh. The advantage of our method lies in it being highly cost and time effective, as we employ a three-point compact stencil, thereby reducing the algebraic calculations considerably. The proposed method which is applicable to singular, boundary layer and singularly perturbed problems is a research gap which we overcame by proposing this new compact spline method.
The space-time spectral collocation method was initially presented for the 1-dimensional sine-Gordon equation. In this article, we introduce a space-time spectral collocation method for solving the 2-dimensional nonli...
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The space-time spectral collocation method was initially presented for the 1-dimensional sine-Gordon equation. In this article, we introduce a space-time spectral collocation method for solving the 2-dimensional nonlinear Riesz space fractional diffusion equations. The method is based on a Legendre-Gauss-Lobatto spectral collocation method for discretizing spatial and the spectral collocation method for the time nonlinear first-order system of ordinary differential equation. Optimal priori error estimates in L-2 norms for the semidiscrete formulation and the uniqueness of the approximate solution are derived. The method has spectral accuracy in both space and time, and the numerical results confirm the statement.
We give a numerical approximation of the solution of a high-order nonlinearinitial-value problem by making use of certain properties of an adequate Schauder basis. (c) 2008 Elsevier B.V. All rights reserved.
We give a numerical approximation of the solution of a high-order nonlinearinitial-value problem by making use of certain properties of an adequate Schauder basis. (c) 2008 Elsevier B.V. All rights reserved.
A numerical method for solving nonlinear initial-value problems is proposed. The Lane-Emden type equations which have many applications in mathematical physics are then considered. The method is based upon hybrid func...
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A numerical method for solving nonlinear initial-value problems is proposed. The Lane-Emden type equations which have many applications in mathematical physics are then considered. The method is based upon hybrid function approximations. The properties of hybrid of block-pulse functions and Lagrange interpolating polynomials are presented and are utilized to reduce the computation of nonlinear initial-value problems to a system of non-algebraic equations. The method is easy to implement and yields very accurate results. (C) 2008 Published by Elsevier B.V.
In this work we obtain an approximation of the solution of a nonlinearinitial-value problem, by means of certain Schauder basis associated in a natural way with that differential problem. (c) 2005 Elsevier Ltd. All r...
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In this work we obtain an approximation of the solution of a nonlinearinitial-value problem, by means of certain Schauder basis associated in a natural way with that differential problem. (c) 2005 Elsevier Ltd. All rights reserved.
An extension of the method of quasilinearization has been applied to first-order nonlinear initial-value problems (IVP for short). It has been shown that there exist monotone sequences which converge rapidly to the un...
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An extension of the method of quasilinearization has been applied to first-order nonlinear initial-value problems (IVP for short). It has been shown that there exist monotone sequences which converge rapidly to the unique solution of IVP.
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