Numerical Methods for Ordinary Differential Equations with Two Parameters
Explicit Euler method, implicit Euler method, trapezoidal rule and midpoint rule are wildly-used and well-known numerical methods for ordinary differential equations. Methods with two parameters are constructed in this paper, whose error analysis is also given by Taylor expansion. The new constructed methods include and extend the 4 well-known methods, and the error analysis with parameters brings us convenience for the error analysis of numerical methods. At last, we give three original methods, whose orders can be gotten directly by the error analysis with parameters.
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This paper is supported by Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (PHR200906210), Funding Project for Base Construction of Scientific Research of Beijing Municipal Commission of Education)(WYJD200902), Beijing Philosophy and Social Science Planning Project (09BaJG258) and Funding Project for Science and Technology Program of Beijing Municipal Commission of Education (KM200910037002).
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