Numerical Solution and Stability Analysis for Burger's-Huxley Equation

Manaa, Saad A.; Saleem, Farhad M.

doi:10.33899/csmj.2009.163797

Cited by 1 publication

(1 citation statement)

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“…As the equations such as and are nonlinear parabolic equations, to analyze their stability using Von Neumann criterion, it's required that we linearize these problems to study its stability properties. To do this, we eliminate the nonlinear terms , we have

u_{t} = u_{x x} + β u,

where

β

is a constant that gives the following relation

\frac{U_{j}^{n + 1} - U_{j}^{n}}{k} = {(U''_{j})}^{n} + β U_{j}^{n},

using we have

\begin{matrix} left \\ \frac{(c_{j - 1}^{n + 1} + 4 c_{j}^{n + 1} + c_{j + 1}^{n + 1}) - (c_{j - 1}^{n} + 4 c_{j}^{n} + c_{j + 1}^{n})}{k} = (\frac{6}{h^{2}}) (c_{j - 1}^{n} - 2 c_{j}^{n} + c_{j + 1}^{n}) \\ + β (c_{j - 1}^{n} + 4 c_{j}^{n} + c_{j + 1}^{n}), \end{matrix}

then substituting Eq. in we have

ξ (4 + 2 cos θ) - (4 + 2 cos θ)

…”

Section: Stability Analysis Of the Numerical Schemementioning

confidence: 99%

Applications of cubic B‐splines collocation method for solving nonlinear inverse parabolic partial differential equations

Pourgholi

Saeedi

2016

Numerical Methods Partial

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In this article, we discuss a numerical method for solving some nonlinear inverse parabolic partial differential equations with Dirichlet's boundary conditions. The approach used, is based on collocation of cubic B-splines over finite elements, so we have continuity of the dependent variable and its first two derivatives throughout the solution range. We apply cubic B-splines for spatial variable and derivatives, which produce an ill-posed system. We solve this system using the Tikhonov regularization method. The accuracy of the proposed method is demonstrated by applying it on two test problems. The figures and comparisons have been presented for clarity. Also the stability of this method has been discussed. The main advantage of the resulting scheme is that the algorithm is very simple, so it is very easy to implement.

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