THE ORDER AND ERROR CONSTANT OF A RUNGE-KUTTA TYPE METHOD FOR THE NUMERICAL SOLUTION OF INITIAL VALUE PROBLEM
DOI:
https://doi.org/10.33003/fjs-2020-0402-256Keywords:
Convergence, initial value problems, step number, differential equationAbstract
Implicit Runge- Kutta methods are used for solving stiff problems which mostly arise in real life situations. Analysis of the order, error constant, consistency and convergence will help in determining an effective Runge- Kutta Method (RKM) to use. Due to the loss of linearity in Runge –Kutta Methods and the fact that the general Runge –Kutta Method makes no mention of the differential equation makes it impossible to define the order of the method independently of the differential equation.
In this paper, we examine in simpler details how to obtain the order, error constant, consistency and convergence of a Runge -Kutta Type method (RKTM) when the step number .
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