A Numerical Solver for First Order Initial Value Problems of Ordinary Differential Equation Via the Combination of Chebyshev Polynomial and Exponential Function

R. Ogunrinde, K. S. Olayemi, I. Isah, A. Salawu
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引用次数: 3

Abstract

Purpose: The purpose of this study is to derive a numerical solver for first order initial value problems of ordinary differential equation via the combination of Chebyshev polynomial and exponential function.Methodology: A new numerical method for solving Initial Value Problems of first order ordinary differential equation is developed. The method is based on finite difference method with a combination of Chebyshev polynomials and exponential function as interpolant. The accuracy, stability, consistency and convergence of the derived scheme were investigated. Numerical experiment was carried out by solving some test problems using the derived scheme.Findings: Results of the numerical experiment revealed that the derived method compared favourably with exact solutions and also performs better than some existing methods for solving initial value problems of first order. Unique Contribution to theory, practice and policy: The study therefore concludes that the method solves problems to expected level of accuracy and can thus be considered among the numerous methods suitable for solving IVPs of first order.
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利用切比雪夫多项式与指数函数组合求解常微分方程一阶初值问题
目的:利用切比雪夫多项式与指数函数的结合,导出常微分方程一阶初值问题的数值解。方法:提出了一种新的求解一阶常微分方程初值问题的数值方法。该方法基于有限差分法,以切比雪夫多项式和指数函数的组合作为插值。研究了该格式的精度、稳定性、一致性和收敛性。利用所导出的格式解决了一些试验问题,并进行了数值试验。结果:数值实验结果表明,该方法在求解一阶初值问题时优于精确解,也优于现有的一些方法。对理论、实践和政策的独特贡献:因此,研究得出结论,该方法解决问题的精度达到预期水平,因此可以被认为是适合解决一阶ivp的众多方法之一。
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来源期刊
International Journal of Physical Sciences
International Journal of Physical Sciences 综合性期刊-综合性期刊
自引率
0.00%
发文量
4
审稿时长
24 months
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