Two-order Runge-Kutta Method for systems of ordinary differential equations using Mathematica




















0. 1. 2.
0.1 0.8925 2.57164
0.2 0.714405 3.00638
0.3 0.47236 3.36747
0.4 0.167222 3.68692
0.5 -0.203373 3.98705

Conclusion:   The solution derived using the Runge-Kutta method O("RK_3sys_EN_19.gif") is in the form of a table of the variable functions y(x) and z(x), shown in the second and third columns of the table above, respectively.  Since the  local apriori error of the method is O("RK_3sys_EN_20.gif") (or global error is  O("RK_3sys_EN_21.gif") ) and here h=0.1, then these solutions must be rounded to three symbols after the decimal point.

Graphic of the solution  







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