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POMaxStepSize, MaxSteps seem to have no effect on NDSolve in MATHEMATICA
 

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  1. POMaxStepSize, MaxSteps seem to have no effect on NDSolve in MATHEMATICA
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    <p>I am a novice at mathematica so please bear with me!</p> <p>I am trying to solve a nonlinear PDE in mma using NDSolve. The solution process is cut short because of singularities occurring much before the time for the simulation runs out. I realize that stiff systems that possess such singularities can be dealt with (at least by brute force) by reducing step size.</p> <p>However "MaxSteps" or "MaxStepSize" doesn't seem to have a tangible effect on my code.</p> <p>What gives? Any other method that I might be missing?</p> <p>**</p> <h2>CODE:</h2> <p>**</p> <pre><code>Needs["VectorAnalysis`"] Needs["DifferentialEquations`InterpolatingFunctionAnatomy`"]; Clear[Eq4, EvapThickFilm, h, S, G, E1, K1, D1, VR, M, R] Eq4[h_, {S_, G_, E1_, K1_, D1_, VR_, M_, R_}] := \!\( \*SubscriptBox[\(\[PartialD]\), \(t\)]h\) + Div[-h^3 G Grad[h] + h^3 S Grad[Laplacian[h]] + (VR E1^2 h^3)/(D1 (h + K1)^3) Grad[h] + M (h/(1 + h))^2 Grad[h]] + E1/( h + K1) + (R/6) D[D[(h^2/(1 + h)), x] h^3, x] == 0; SetCoordinates[Cartesian[x, y, z]]; EvapThickFilm[S_, G_, E1_, K1_, D1_, VR_, M_, R_] := Eq4[h[x, y, t], {S, G, E1, K1, D1, VR, M, R}]; TraditionalForm[EvapThickFilm[S, G, E1, K1, D1, VR, M, R]]; L = 318; TMax = 7.0; Off[NDSolve::mxsst]; Clear[Kvar]; Kvar[t_] := Piecewise[{{0.01, t &lt;= 4}, {0.05, t &gt; 4}}] (*Ktemp = Array[0.001+0.001#^2&amp;,13]*) hSol = h /. NDSolve[{ (*S,G,E,K,D,VR,M*) EvapThickFilm[1, 3, 0.1, Kvar[t], 0.01, 0.1, 0, 160], h[0, y, t] == h[L, y, t], h[x, 0, t] == h[x, L, t], (*h[x,y,0] == 1.1+Cos[x] Sin[2y] *) h[x, y, 0] == 1 + (-0.25 Cos[2 \[Pi] x/L] - 0.25 Sin[2 \[Pi] x/L]) Cos[ 2 \[Pi] y/L] }, h, {x, 0, L}, {y, 0, L}, {t, 0, TMax} ][[1]] </code></pre> <h2>Error message:</h2> <p>NDSolve::ndsz: At t == 2.366570254802048`, step size is effectively zero; singularity or stiff system suspected. >></p> <p>NDSolve::eerr: Warning: Scaled local spatial error estimate of 571455.5042645375<code>at t = 2.366570254802048</code> in the direction of independent variable x is much greater than prescribed error tolerance. Grid spacing with 19 points may be too large to achieve the desired accuracy or precision. A singularity may have formed or you may want to specify a smaller grid spacing using the MaxStepSize or MinPoints method options. >></p>
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    1. USDr. belisarius
    1. USdrN
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    1. COUsually, the shorter and more to the point your posted code is, the better answers you'll get
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      1. POMaxStepSize, MaxSteps seem to have no effect on NDSolve in MATHEMATICA
      1. USDr. belisarius
    2. COThanks for the constructive criticism.
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      1. POMaxStepSize, MaxSteps seem to have no effect on NDSolve in MATHEMATICA
      1. USdrN
 

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