Consistency, Stability, and Convergence of Newton-Cotes Rule for Nonlinear Goursat Problem

机译：非线性Goursat问题的牛顿型号规则的一致性，稳定性和融合

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Many nonlinear problems that arise in various sciences and engineering fields can be described by the Goursat partial differential equation. The study of this problem has not received much attention especially in theoretical parts. The proposed scheme is supported by examining a nonlinear Goursat problem and the verification of these theoretical results from several series of numerical experiments are discussed. Results obtained show that the proposed new scheme is consistent through Taylor series expansion and stable by using the von Neumann analysis and essence of stability. In addition to that, by looking at the trend of the numerical results it is proved that the new scheme is also convergent.

机译：可以通过Goursat偏微分方程描述各种科学和工程领域中出现的许多非线性问题。对这个问题的研究尤其是在理论部分中的关注。通过检查非线性Goursat问题，并讨论了几次数值实验的这些理论结果的验证，支持该方案。得到的结果表明，通过使用von neumann分析和稳定性的本质，拟议的新方案是通过泰勒序列的膨胀和稳定的一致性。除此之外，通过查看数值结果的趋势，证明新方案也是会聚。

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《International Conference on Education, Mathematics and Science》|2017年|1 v. (various pagings) :|共6页
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作者
Ros Fadilah Deraman; Noraini Kasron; Erni Suryani Suharto; Mohd Agos Salim Nasir;
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中图分类 O1-532;
关键词
Goursat problem; partial differential equation; numerical integration; Newton-Cotes formula; consistency; stability; convergence;

机译：Goursat问题;部分微分方程;数值整合;牛顿 - Cotes公式;一致性;稳定性;收敛;

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2. The superconvergence of the Newton-Cotes rule for Cauchy principal value integrals [J] . Liu D., Wu J., Yu D. Journal of Computational and Applied Mathematics . 2010,第3期

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3. The superconvergence of composite Newton-Cotes rules for Hadamard finite-part integral on a circle [J] . Xiaoping Zhang Jiming Wu Dehao Yu Computing. Archives for Informatics and Numerical Computation . 2009,第3期

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4. Consistency, Stability, and Convergence of Newton-Cotes Rule for Nonlinear Goursat Problem [C] . Ros Fadilah Deraman, Noraini Kasron, Erni Suryani Suharto, International Conference on Education, Mathematics and Science . 2017

机译：非线性Goursat问题的牛顿型号规则的一致性，稳定性和融合
5. Bayesian inference with mixtures of logistic regression: Functional approximation, statistical consistency and algorithmic convergence. [D] . Ge, Yang. 2008

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7. Numerical Solution Of A Linear Goursat Problem Stability,Consistency And Convergence . [O] . Md. Ismail Ahmad Izani, Salim Nasir Mohd Agos 2004

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8. Semi-Discrete Approximations to Nonlinear Systems of Conservation Laws; Consistency and L(Infinity)-Stability Imply Convergence [R] . Tadmor, E. 1988

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Consistency, Stability, and Convergence of Newton-Cotes Rule for Nonlinear Goursat Problem

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