DEVELOPMENT AND ANALYSIS OF A HIGH-ACCURACY THIRD-ORDER RUNGE–KUTTA METHOD FOR NON-AUTONOMOUS INITIAL VALUE PROBLEMS
DOI:
https://doi.org/10.71146/kjmr901Keywords:
Numerical Method, Third-Order, Local Truncation Error, Consistency, StabilityAbstract
New class of explicit and single step third order improved scheme developed to numerically integrate initial value problems for differential equations in nature ordinary. The stability requirements of the enhanced plan are explored, and stability region of the same is plotted. Third order accuracy of the improved scheme is also confirmed by error analysis performed. The partial derivative with respect to the space dependent variable has been introduced inside the function evaluation which boasts the convergence and efficiency of the proposed scheme. Few problems have been tested to determine absolute errors named as last and maximum. Approximate solutions are provided and demonstrate the accuracy the better scheme. The performance of the improved and the existing schemes with same order of local accuracy are discussed. Based on the results, the improved scheme gives the better result in comparison of other available schemes in literature. With the help of software MATLAB 2023a, the numerical results and graphical representation of the newly proposed scheme are justified.
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Copyright (c) 2026 Muhammad Daud Kandhro, Naveed Ahmed Tunio, Raja Faisal Soomro, Muhammad Imran Soomro (Author)
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