The Efficiency of Block Hybrid Method for Solving Malthusian Growth Model and Prothero-Robinson Oscillatory Differential Equations

The efficiency of block hybrid method for solving Malthusian Growth Model, Prothero-Robinson equation and highly stiff oscillatory differential equations was proposed using a power series polynomial through interpolation and collocation. The new method's basic properties, including order, error constant, consistency, zero-stability, and stability regions, were comprehensively analyzed and satisfied all necessary conditions for analysis. Tested on various real-life problems, the new method demonstrated superior performance compared to existing techniques. The study highlights the innovative approach's enhanced convergence and stability properties, providing a more reliable numerical analysis tool for researchers and practitioners. Practical applications validate the method's effectiveness, showcasing its superior performance across different examples and establishing it as a highly effective solution for Malthusian growth model and oscillatory differential equations.