THE DERIVED EXPLICIT FOURTH-STAGE SECOND-ORDER RUNGE-KUTTA METHOD IS CONSISTENT AND CONVERGENT - Christopher, Esekhaigbe Aigbedion; Edward, Okodugha (Journal of Advance Research in Mathematics and Statistics (ISSN 2208-2409), 2023)
The purpose of this paper is to analyze the consistency and convergence of an explicit fourth-stage second-order Runge-Kutta method derived using Taylor series expansion by varying parameters. The analysis revealed that the method is consistent and convergent. These properties are key and vital for any numerical method to possess for it to be capable of handling initial value problems. The implementation of this method on initial-value problems has been done in previous paper, and it revealed that the method compared favorably well with the other existing explicit Runge Kutta method of the same order. Hence, as a result of the convergence and consistency of the method, it will definitely be reliable and dependable.