Development of an explicit iterative numerical scheme over the modified euler's method

Tuljaram Meghwar; Rahim Bux Khokhar; Asif Ali Shaikh; Evren Hincal; Muhammad Anwar Solangi; Prem Kumar

Tuljaram Meghwar Department of Basic Sciences & Related Studies, Mehran Univeristy of Engineering and technology,Jamshoro, Sindh,Pakistan

Rahim Bux Khokhar Department of Basic Sciences & Related Studies, Mehran Univeristy of Engineering and technology,Jamshoro, Sindh,Pakistan

Asif Ali Shaikh Department of Basic Sciences & Related Studies, Mehran Univeristy of Engineering and technology,Jamshoro, Sindh,Pakistan; Department of Mathematics, Near East University,99138 Mersin,Turkey

Evren Hincal Department of Mathematics, Near East University,99138 Mersin,Turkey

Muhammad Anwar Solangi Department of Basic Sciences & Related Studies, Mehran Univeristy of Engineering and technology,Jamshoro, Sindh,Pakistan

Prem Kumar Department of Basic Sciences & Related Studies, Mehran Univeristy of Engineering and technology,Jamshoro, Sindh,Pakistan; Department of Mathematical and Statistical Sciences, University of Alberta,Edmonton,Canada

Major goal of this study, to propose a new explicit iterative numerical scheme that can substitute the modified Euler's method (MEM) for initial value issues in ordinary diferential equations. This iterative strategy has been suggested by substituting the main slope of the MEM and the slope of the explicit forward Euler's method for the inner slope h(µ i, vi) of the MEM. Accuracy and stability are used to determine uniqueness in work. There are a few low accuracy and stability modified Euler technique variants that may be found in the literature. This study presents an innovative approach with the goal of obtaining greater accuracy and stability. The suggested iterative scheme's performance was evaluated by examining various numerical factors connected to the numerical method, and it was discovered that it is more accurate and consistent with the numerical order of convergence two. The proposed scheme's derived stability region and interval of stability region are greater than those technique which were present in literature previously, such as the Euler's method (EM), improved Euler's method (IEM), modified Euler's method (MEM), modified improved modified Euler's method (MIME), and improved modified Euler's method (IMEM). The proposed scheme generally showed greater accuracy in each initial value problem (IVPs) after being evaluated with several open literature initial value problems using various step sizes.