Numerical Application of Enright's Linear Multistep Method on Oscillatory Differential Equations
Keywords:
Oscillatory Differential Equations, Numerical Methods, Enright Linear Multistep Method, Block Hybrid Method, Interpolation and Collocation.Abstract
Oscillatory differential equations play a vital role in modeling natural and physical phenomena in fields such as biology, circuit theory, and fluid dynamics. These equations often lack analytical solutions, necessitating numerical methods for resolution. This study focuses on the development and application of a continuous Enright linear multistep block hybrid method to solve first-order oscillatory differential equations. The method leverages interpolation and collocation techniques to generate a high-order, stable, and accurate numerical scheme. The basic properties, including order, consistency, zero-stability, convergence and the region of absolute stability, are analyzed to validate the method. Numerical experiments are conducted to compare the new method's accuracy and computational efficiency against existing approaches, demonstrating its superior performance in solving oscillatory problems.
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