Timeline for Solution of Riccati equation of y'[z]==R(z) y(z)^2+Q(z) y(z)+P(z) type
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 20, 2019 at 12:57 | comment | added | Michael E2 | @DarkKnight45 For further discussion, see reference.wolfram.com/language/tutorial/NDSolveVectorNorm.html, mathematica.stackexchange.com/questions/9161/…, mathematica.stackexchange.com/questions/118249/…, and mathematica.stackexchange.com/a/138634/4999 | |
| May 20, 2019 at 10:59 | comment | added | Michael E2 |
Here's a simple example of how decreasing step size eventually converges toward the exact solution $y = e^{-x}$: Table[ ListLinePlot[ NDSolveValue[{y'[x] + y[x] == 0, y[0] == 1}, y, {x, 0, 60}, Method -> {"FixedStep", Method -> "ExplicitRungeKutta"}, StartingStepSize -> 1.5^k], InterpolationOrder -> 3, PlotLabel -> Row[{"Step size ", 1.5^k}]], {k, 4, -1, -1}]
|
|
| May 20, 2019 at 10:56 | comment | added | Michael E2 |
@DarkKnight45 It should be, but I suppose it depends on what the editors/reviews understand about numerical analysis and Mathematica. With most numerical ODE solvers, each step incurs an error, in which the compute solution steps off the current solution curve onto another that is "near by." How near by depends on the step size. The smaller the step, the smaller the maximum error. As the step size decreases, the "randomness" should go away and the computed solution should converge to a stable result. AccuracyGoal and PrecisionGoal are one way for the user to control the step size.
|
|
| May 20, 2019 at 5:47 | comment | added | Dark Knight45 | In mathematica changing this accuracy goal slightly changes the results is such randomness permissible in scientific publication | |
| Apr 24, 2019 at 4:05 | vote | accept | Dark Knight45 | ||
| Apr 24, 2019 at 4:01 | comment | added | Dark Knight45 | Thanks a Lot.You got it correctly | |
| Apr 24, 2019 at 2:06 | history | answered | Michael E2 | CC BY-SA 4.0 |