Abstract
This research study focuses on a computational strategy of variable step, variable order (CSVSVO) for solving stiff systems of ordinary differential equations. The idea of Newton’s interpolation formula combine with divided difference as the basis function approximation will be very useful to design the method. Analysis of the performance strategy of variable step, variable order of the method will be justified. Some examples of stiff systems of ordinary differential equations will be solved to demonstrate the efficiency and accuracy.
Highlights
In diverse applied sciences, like chemical kinetics, mass-spring-damper systems, and control system analysis, we find systems of differential equations whose analytical solutions comprise terms with magnitudes that change at rates that are substantially unlike
This aspect implements the computational strategy of variable step, variable order for solving stiff systems of ordinary differential equations
The different application problems of stiff system of ordinary differential equations were implemented on diverse convergence criteria of the following: 10−3, 10−3, 10−4, 10−5, 10−6, 10−7, 10−8, 10−9, 10−10 and 10−11
Summary
Like chemical kinetics, mass-spring-damper systems, and control system analysis, we find systems of differential equations whose analytical solutions comprise terms with magnitudes that change at rates that are substantially unlike. In cases of a quickly decaying transient analytical solution, a sure computational technique turns unstable except the step length is immoderately small. Explicit techniques universally are submitted to this stability control, which necessitates the usage of very small step length necessarily improve the amount of functions to find the analytic solution, and as such stimulates round-off error to spring up, having bounded accuracy and efficiency. Again, are release of stability limitations and are favourable for computing stiff systems differential equations [27]. ), ym(x) where the yi(x) are differentiable functions that gratifies (1) on I[1] for details
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