Development of Improved Scheme for Numerical Integration of Autonomous and Non-Autonomous Initial Value Problems

Abstract

:In this research study, an explicit and single stepnew third order improved scheme for numerical integration of autonomous and non-autonomous initial value problemsalso called Cauchy problems in ordinary differential equations has been developed. Linear stability analysis with corresponding stability region is drawn and error analysis has been provided to confirm third order accuracy of the improved scheme. Inclusion of a partial derivative with respect to the dependent variable with in two slopes of the improved scheme has improved its efficiency in terms of local and global truncation errors. Finally, numerical examples are provided to show performance of the improved scheme in comparison with other existing methods having same order of local accuracy. Throughout the study it has been observed from the results and comparison of the improved scheme that develop algorithm is superior to some existing numerical methods of same order in term of error analysis as well as accuracy viewpoint.The software MATLAB is used to justify the results and graphical representation of the improved scheme.