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

























1 1. 2.
1.1 0.886873 2.15592
1.2 0.744792 2.32486
1.3 0.569252 2.50858
1.4 0.355089 2.70883
1.5 0.0964108 2.92739

Conclusion:   The solution derived using the Runge-Kutta method O("RK_5sys_EN_24.gif") is in the form of a table of the 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_5sys_EN_25.gif") (or global error is  O("RK_5sys_EN_26.gif") ) and here h=0.1, then these solutions must be rounded to three symbols after the decimal point.

Graphics of the solution     





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