New algorithms for numerical integration and ODE solutions

03152014, 06:31 PM
Post: #5




RE: New algorithms for numerical integration and ODE solutions
When I ran your mod using Gauss2 on Sheet10, I got a result that was not very accurate. the result was something like 0.69.
Because of the small slope at zero, the first value of h was 1000, then Y2=0 and the calculation of h is exited. X2 is then reduced to 5 (XMax), then the Gauss algorithm calculates the integral in one interval from 0 to 5. I recommend modifying the calculation of h as follows: XMaxDelta = (Xmax  X1) / 5 ' Put an upper limit on the interval size h = 2 * Abs(YMaxDelta / MyDx(sFx, X1)) If (h > XMaxDelta) Then h = XMaxDelta For i = 1 To 100 ' prevent infinite loop (may not be necessary) h = h / 2 X2 = X1 + h Y2 = MyFx(sFx, X2) If (Abs(Y2  Y1) <= YMaxDelta) Then Exit For Next i A better way might be to remove EPSILON from MyDx (allow that function to be as accurate as possible) and calculate 1/h first to avoid a divide by zero, then limit 1/h. 

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