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A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations

机译：非线性发展抛物型方程的二元Chebyshev谱配置拟线性化方法。

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This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.

机译：本文提出了一种求解高阶非线性演化偏微分方程（NPDEs）的新方法。该方法结合了准线性化，Chebyshev频谱配置方法和双变量Lagrange插值。在本文中，我们使用该方法求解了几个非线性演化方程，例如修正的KdV-Burgers方程，高度非线性的修正KdV方程，Fisher方程，Burgers-Fisher方程，Burgers-Huxley方程和Fitzhugh-Nagumo方程。将结果与文献中已知的精确分析解决方案进行比较，以确认该方法的准确性，收敛性和有效性。数值结果与精确度高的精确解之间存在一致性。生成表格以表示该方法的准确性顺序；展示了收敛图以验证方法的收敛性，并给出了误差图，以表明本研究结果与文献中的已知结果之间存在极好的一致性。

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S. S. Motsa; V. M. Magagula; P. Sibanda;
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年(卷),期 -1(2014),-1
年度 -1
页码 581987
总页数 13
原文格式 PDF
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专利

1. A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations [J] . S. S.Motsa, V. M.Magagula, P.Sibanda ScientificWorldJournal . 2014,第3期

机译：非线性切口散谱搭配Quasilinearization方法，用于非线性演化抛物线方程
2. Numerical solutions of some nonlinear evolution equations by Chebyshev spectral collocation methods [J] . A. H. KHATER, R. S. TEMSAH International journal of computer mathematics . 2007,第3期

机译：用Chebyshev谱配置方法求解某些非线性发展方程的数值解。
3. A New Chebyshev Spectral-collocation Method for Solving a Class of One-dimensional Linear Parabolic Partial Integro-differential Equations [J] . Galal I. El–Baghdady, M. S. El–Azab British Journal of Mathematics & Computer Science . 2014,第3期

机译：一类一维线性抛物型偏微分积分方程的Chebyshev谱配置新方法
4. Nonlinear elasto-plastic analysis of axisymmetric spherical shell by Chebyshev spectral collocation method under the pulsating forces [C] . Mohamadreza Salehi Barzegar, Alireza Nadaf Oskooe, Kaveh Najafi, International Conference on Mechanical and Aerospace Engineering . 2012

机译：Chebyshev光谱剥离法在脉动力下的非线性弹性塑性分析
5. Collocation methods for linear parabolic partial differential equations. [D] . Zheng, Qiang. 2006

机译：线性抛物型偏微分方程的配置方法。
6. Jacobi spectral collocation method for the approximate solution of multidimensional nonlinear Volterra integral equation [O] . Yunxia Wei, Yanping Chen, Xiulian Shi, -1

机译：多维非线性Volterra积分方程近似解的Jacobi谱配点法
7. Solving Nonlinear Parabolic Partial Differential Equations Using Multidomain Bivariate Spectral Collocation Method [O] . Sandile Sydney Motsa, Samuel Felix Mutua, Shateyi Stanford 2016

机译：利用多麦田双抗体谱剥离方法求解非线性抛物局部微分方程
8. Numerical Solution of Nonlinear Volterra Integral Equations of the Second Kind by Collocation and Iterated Collocation Methods [R] . Blom, J. G., Brunner, H. 1985

机译：第二类非线性Volterra积分方程的配置和迭代配置方法的数值解

A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations

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