 

Second Order RungeKutta Method (RK2) to Solve ODE Suppose we have ODE then Formula: Where and Other variation name: Improve Euler method, Heun's method, Midpoint method Error term: , correct up to the second order term in Taylor series expansion. The Taylor series expansion is The computation is using spreadsheet that can be downloaded here
Example: , set , with initial condition . The few first results and the graph of solution are given below. Note that after , the solution is not correct. See Comparison.
Expanding the order RungeKutta formula, we have Second term of the right hand side [ ] is the estimated range difference. The estimated range difference is computed based on a half of the slope at the beginning of the interval and the slope in the middle of the interval , as illustrated in the figure below <Previous  Next  Contents>
Preferable reference for this tutorial is Teknomo, Kardi. Solving Ordinary Differential Equation (ODE). http:\\people.revoledu.com\kardi\ tutorial\ODE\ 



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