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Stable Computer Method for Solving Initial Value Problems with Engineering Applications

Computer systems Science & Engineering 2023年第6期45卷 2617-2633页

作者： Mudassir Shams Nasreen Kausar Ebru Ozbilge Alper Bulut Department of Mathematics and Statistics Riphah International UniversityI-14Islamabad44000Pakistan Department of Mathematics Yildiz Technical UniversityFaculty of Arts and ScienceEsenler34210IstanbulTurkey Department of Mathematics&Statistics American University of the Middle EastEgaila54200Kuwait

Engineering and applied mathematics disciplines that involve differential equations in general,and initial value problems in particular,include classical mechanics,thermodynamics,electromagnetism,and the general theory of relativity.A reliable,stable,efficient,and consistent numerical scheme is frequently required for modelling and simulation of a wide range of real-world problems using differential *** this study,the tangent slope is assumed to be the contra-harmonic mean,in which the arithmetic mean is used as a correction instead of Euler’s method to improve the efficiency of the improved Euler’s technique for solving ordinary differential equations with initial *** stability,consistency,and efficiency of the system were evaluated,and the conclusions were supported by the presentation of numerical test applications in *** to the stability analysis,the proposed method has a wider stability region than other well-known methods that are currently used in the literature for solving initial-value *** validate the rate convergence of the numerical technique,a few initial value problems of both scalar and vector valued types were *** proposed method,modified Euler explicit method,and other methods known in the literature have all been used to calculate the absolute maximum error,absolute error at the last grid point of the integration interval under consideration,and computational time in seconds to test the *** lorentz system was used as an example to illustrate the validity of the solution provided by the newly developed *** method is determined to be more reliable than the commonly existing methods with the same order of convergence,as mentioned in the literature for numerical calculations and visualization of the results produced by all the methods discussed,Mat Lab-R2011b has been used.

关键词： Local truncation error consistency computational time stability lorentz system

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