Journal ArticleDOI
High accuracy cubic spline finite difference approximation for the solution of one-space dimensional non-linear wave equations
R. K. Mohanty,Venu Gopal +1 more
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TLDR
The proposed method when applied to a linear hyperbolic equation is shown to be unconditionally stable andumerical results are provided to justify the usefulness of the proposed method.About:
This article is published in Applied Mathematics and Computation.The article was published on 2011-12-15. It has received 29 citations till now. The article focuses on the topics: Monotone cubic interpolation & Partial differential equation.read more
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Polynomial and nonpolynomial spline methods for fractional sub-diffusion equations
TL;DR: In this paper, the authors consider one-dimensional fractional sub-diffusion equations on an unbounded domain and analyze the numerical solution of the problem by polynomial and nonpolynomial spline methods.
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The impact of LRBF-FD on the solutions of the nonlinear regularized long wave equation
TL;DR: In this article, the authors developed a method for the numerical solution of the nonlinear regularized long wave equation, which discretizes the unknown solution in two main schemes: time discretization by means of an implicit method based on the $$\theta $$¯¯ -weighted and finite difference methods, while the spatial discretisation is described with the help of the finite difference scheme derived from the local radial basis function method.
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Tension spline method for solution of non-linear Fisher equation
TL;DR: The three time-level implicit method based on the non-polynomial cubic tension spline is developed for the solution of thenon-linear reaction-diffusion equation.
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Numerical solution for the Kawahara equation using local RBF-FD meshless method
TL;DR: The main goal in this work is to develop the RBF-FD method in order to obtain numerical solution for the Kawahara equation as a time dependent partial differential equation that appears in the shallow water and acoustic waves in plasma.
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Numerical simulation on hyperbolic diffusion equations using modified cubic B-spline differential quadrature methods
R. C. Mittal,Sumita Dahiya +1 more
TL;DR: A modified cubic B-spline differential quadrature method (MCB-DQM) is proposed to solve a hyperbolic diffusion problem in which flow motion is affected by both convection and diffusion.
References
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Journal ArticleDOI
Piecewise Cubic Interpolation and Two-Point Boundary Problems
TL;DR: Cubic splines are employed, experimentally, to approximate to the solution of a simple two-point boundary value problem for a linear ordinary differential equation, and results are encouraging.
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The use of cubic splines in the solution of two-point boundary value problems
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New unconditionally stable difference schemes for the solution of multi-dimensional telegraphic equations
TL;DR: New unconditionally stable implicit difference schemes for the numerical solution of multi-dimensional telegraphic equations subject to appropriate initial and Dirichlet boundary conditions are discussed.
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An unconditionally stable difference scheme for the one-space-dimensional linear hyperbolic equation
TL;DR: An implicit three-level difference scheme of O(k2 + h2) is discussed for the numerical solution of the linear hyperbolic equation utt + 2αut + β2u = uxx + f(x, t), α > β ≥ 0, subject to appropriate initial and Dirichlet boundary conditions, where α and β are real numbers.