# THE ORDER AND ERROR CONSTANT OF A RUNGE-KUTTA TYPE METHOD FOR THE NUMERICAL SOLUTION OF INITIAL VALUE PROBLEM

Keywords: Convergence, initial value problems, step number, differential equation

### Abstract

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 â€“Kutta Methods and the fact that the general Runge â€“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  .

### References

Butcher, J.C (2008). Numerical methods for ordinary differential equations. John Wiley & Sons.

Kulikov, G. Yu. (2003). â€œSymmetric Runge Kutta Method and their stabilityâ€. Russ J. Numeric Analyze and Maths Modelling. 18(1): 13-41

Yahaya, Y.A. & Adegboye, Z.A. (2011). Reformulation of quadeâ€™s type four-step block hybrid multstep method into runge-kutta method for solution of first and second order ordinary differential equations. Abacus, 38(2), 114-124.

Yahaya Y.A. and Adegboye Z.A. (2013). Derivation of an implicit six stage block runge kutta type method for direct integration of boundary value problems in second order ode using the quade type multistep method. Abacus, 40(2), 123-132.
Published
2020-10-13
How to Cite
MuhammadR. (2020). THE ORDER AND ERROR CONSTANT OF A RUNGE-KUTTA TYPE METHOD FOR THE NUMERICAL SOLUTION OF INITIAL VALUE PROBLEM. FUDMA JOURNAL OF SCIENCES, 4(2), 743 - 748. https://doi.org/10.33003/fjs-2020-0402-256
Section
Research Articles