A COMPARATIVE STUDY ON NUMERICAL SOLUTIONS OF INITIAL VALUE PROBLEMS OF DIFFERENTIAL EQUATIONS USING THE THREE NUMERICAL METHODS
Numerical methods are crucial for solving ordinary differential equations (ODEs) that frequently arise in various fields of science and engineering. This study compares three numerical methods: the fourth-order Runge-Kutta method (RK4), the fourth-order Runge-Kutta Contra-harmonic Mean method (CoM4)...
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Universitas Pattimura
2025-04-01
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| Series: | Barekeng |
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| Online Access: | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/15592 |
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| author | Marsudi Marsudi Isnani Darti |
| author_facet | Marsudi Marsudi Isnani Darti |
| author_sort | Marsudi Marsudi |
| collection | DOAJ |
| description | Numerical methods are crucial for solving ordinary differential equations (ODEs) that frequently arise in various fields of science and engineering. This study compares three numerical methods: the fourth-order Runge-Kutta method (RK4), the fourth-order Runge-Kutta Contra-harmonic Mean method (CoM4), and the fourth-order Adam-Bashforth-Moulton method (ABM4) in solving initial value problems of ODEs. Three IVPs of ODEs have been solved with varying step sizes using the three methods that have been proposed, and the solutions for each step size are examined. Numerical comparisons between RK4, CoM4, and ABM4 methods have been presented to solve three initial problems of ODE. Simulation results show that each method has advantages and limitations depending on the type of ODE being solved. We find that for very small step sizes, the numerical solutions agree the best with the exact solution. As such, all three proposed approaches are sufficient to solve the IVP ODE accurately and efficiently. Among the three proposed methods, we observe that the mean absolute error for the RK4 method is the smallest, followed by the ABM4 method. |
| format | Article |
| id | doaj-art-e81c84b84bc94204893c6bb9db64b86b |
| institution | Kabale University |
| issn | 1978-7227 2615-3017 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Universitas Pattimura |
| record_format | Article |
| series | Barekeng |
| spelling | doaj-art-e81c84b84bc94204893c6bb9db64b86b2025-08-20T03:37:34ZengUniversitas PattimuraBarekeng1978-72272615-30172025-04-011921263127810.30598/barekengvol19iss2pp1263-127815592A COMPARATIVE STUDY ON NUMERICAL SOLUTIONS OF INITIAL VALUE PROBLEMS OF DIFFERENTIAL EQUATIONS USING THE THREE NUMERICAL METHODSMarsudi Marsudi0Isnani Darti1Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya, IndonesiaNumerical methods are crucial for solving ordinary differential equations (ODEs) that frequently arise in various fields of science and engineering. This study compares three numerical methods: the fourth-order Runge-Kutta method (RK4), the fourth-order Runge-Kutta Contra-harmonic Mean method (CoM4), and the fourth-order Adam-Bashforth-Moulton method (ABM4) in solving initial value problems of ODEs. Three IVPs of ODEs have been solved with varying step sizes using the three methods that have been proposed, and the solutions for each step size are examined. Numerical comparisons between RK4, CoM4, and ABM4 methods have been presented to solve three initial problems of ODE. Simulation results show that each method has advantages and limitations depending on the type of ODE being solved. We find that for very small step sizes, the numerical solutions agree the best with the exact solution. As such, all three proposed approaches are sufficient to solve the IVP ODE accurately and efficiently. Among the three proposed methods, we observe that the mean absolute error for the RK4 method is the smallest, followed by the ABM4 method.https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/15592adam-bashforth-moultoninitial value problemsmean absolute errorrunge-kuttarunge-kutta contra-harmonic mean |
| spellingShingle | Marsudi Marsudi Isnani Darti A COMPARATIVE STUDY ON NUMERICAL SOLUTIONS OF INITIAL VALUE PROBLEMS OF DIFFERENTIAL EQUATIONS USING THE THREE NUMERICAL METHODS Barekeng adam-bashforth-moulton initial value problems mean absolute error runge-kutta runge-kutta contra-harmonic mean |
| title | A COMPARATIVE STUDY ON NUMERICAL SOLUTIONS OF INITIAL VALUE PROBLEMS OF DIFFERENTIAL EQUATIONS USING THE THREE NUMERICAL METHODS |
| title_full | A COMPARATIVE STUDY ON NUMERICAL SOLUTIONS OF INITIAL VALUE PROBLEMS OF DIFFERENTIAL EQUATIONS USING THE THREE NUMERICAL METHODS |
| title_fullStr | A COMPARATIVE STUDY ON NUMERICAL SOLUTIONS OF INITIAL VALUE PROBLEMS OF DIFFERENTIAL EQUATIONS USING THE THREE NUMERICAL METHODS |
| title_full_unstemmed | A COMPARATIVE STUDY ON NUMERICAL SOLUTIONS OF INITIAL VALUE PROBLEMS OF DIFFERENTIAL EQUATIONS USING THE THREE NUMERICAL METHODS |
| title_short | A COMPARATIVE STUDY ON NUMERICAL SOLUTIONS OF INITIAL VALUE PROBLEMS OF DIFFERENTIAL EQUATIONS USING THE THREE NUMERICAL METHODS |
| title_sort | comparative study on numerical solutions of initial value problems of differential equations using the three numerical methods |
| topic | adam-bashforth-moulton initial value problems mean absolute error runge-kutta runge-kutta contra-harmonic mean |
| url | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/15592 |
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