Search Results

This problem seems to be really stiff as whuber has pointed out. Using the BDF method and allowing NDSolve to ruminate about the order, didn't quite change the solution (z value where stiffness was e …

First solve this: a = NIntegrate[Sqrt[1 + E^tt^2 Sin[tt^2]], {tt, 0, 1}] And then do this: DSolve[{D[u[t], t] == a u[t], u[0] == 1}, u[t], t] That should solve the problem.

I always wondered if I could start NDSolve from an intermediate time step. What I mean is, in the code sample below, if I were to run my solution from tmin=0 to tmax=2 and then I realize that my sol …

I am trying to check if mass conservation holds by integrating the area under a curve but to no avail. Needs["DifferentialEquations`InterpolatingFunctionAnatomy`"]; Needs["VectorAnalysis`"] Clear[E …

I am solving a non linear partial differential equation with what I call free boundary conditions (solid mechanicists would know this as simply supported). I realized that this boundary condition doe …

Is the EventLocator option not compatible with LSODA on NDSolve. Below is what I tried to do to arrest my simulation if the time step went below a certain value (based on this suggestion). The script …

I've been using Mathematica to solve nonlinear partial differential equations for my doctoral research for the last 2 years or so. I am not an expert in Mathematica or mathematics and I am an engineer …

I notice that off all the Method options available for NDSolve[...], LSODA is invoked quite automatically for stiff equations when Method -> Automatic. Is there a way to set the Method -> LSODA? I as …

I generally use NDSolve for stiff non linear partial differential equations of 4th order. I find that a BDF1 method generally does well to placate my beast of a PDE. I've also tried out "MaxSteps" to …

Very often I solve partial differential equations that are nonlinear and could be up to 4th order. In these cases, it is usual for the solution determined by NDSolve to be stiff during a later stage. …

What is NDSolve's mode of operation? I use it to solve partial differential equations and never gave it too much thought. Recently, I came across this question. Accordingly, I used Trace[...] and re …

I find that with NDSolve[...] while solving a partial differential equation, changing the MaxStepFraction from 1/10 to say 1/60, improves convergence. Without going into too many details about the PD …

I am trying to that using a coarse grid with an explicit method for, say, the advection equation leads to an unstable solution. The trouble is Mathematica avoids unstable solutions with good Methods o …

As prompted by one of the comments, stiffness switching did help some. I usually go with Method->LSODA for stiff equations but tried Method -> {"StiffnessSwitching", Method -> {"ExplicitRun …

I've been playing around with Method in NDSolve[...] and can't quite seem to figure out how to force NDSolve to use a certain difference order with a certain method. For instance, I am trying to val …