Numerical Method to Solve the Cauchy Problem with Previous History

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• 作者：V. A. Prusov ; A. Yu. Doroshenko
• 关键词：ordinary differential equations ; single ; stage multi ; step method ; discretization ; approximation ; convergence ; strong stability
• 刊名：Cybernetics and Systems Analysis
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：53
• 期：1
• 页码：34-56
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Systems Theory, Control; Artificial Intelligence (incl. Robotics); Processor Architectures; Software Engineering/Programming and Operating Systems;
• 出版者：Springer US
• ISSN：1573-8337
• 卷排序：53

文摘

The paper analyzes the theoretical aspects of constructing a family of single-stage multi-step methods for solving the Cauchy problem with prehistory for ordinary differential equations. The authors consider general issues related to discretization, approximation, convergence, and stability. The problem of improving the accuracy of numerical solutions is analyzed in detail. The results presented in the paper are also applicable for the numerical solution of partial differential equations.