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POHow to "embed" Piecewise in NDSolve in Mathematica
 

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  1. POHow to "embed" Piecewise in NDSolve in Mathematica
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    <ol> <li>I am using <code>NDSolve</code> to solve a non-linear partial differential equation. </li> <li>I'd like one of the variables (Kvar) to be a function of the time step currently being solved and hence and using <code>Piecewise</code>. </li> <li>Mathematica generates an error message saying:</li> </ol> <blockquote> <p>SetDelayed::write: Tag Real in 0.05[t_] is Protected. >> NDSolve::deqn: Equation or list of equations expected instead of $Failed in the first argument ....</p> <p>ReplaceAll::reps: ....</p> </blockquote> <p>I haven't included the entire error message for ease of reading.</p> <p>My code is as follows:</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]]; </code></pre> <p>And the second cell where I am trying to implement <code>Piecewise</code> in <code>NDSolve</code>:</p> <pre><code>L = 318; TMax = 7.0; Off[NDSolve::mxsst]; (*Ktemp = Array[0.001+0.001#^2&amp;,13]*) hSol = h /. NDSolve[{ (*S,G,E,K,D,VR,M*) Kvar[t_] := Piecewise[{{0.01, t &lt;= 4}, {0.05, t &gt; 4}}], 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]] hGrid = InterpolatingFunctionGrid[hSol]; </code></pre> <p>PS: I am sorry but the first cell block doesn't display so well here. And thanks to not having enough "reputation", I can't post images.</p> <p>The error message occurs when using the <code>NDSolve</code> cell block.</p>
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    1. USSjoerd C. de Vries
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    1. COTake the definition of Kvar[t_] out of the NDSolve argument list. it will then give a solution. Might need to massage NDSolve settings to get better error estimate and have it run successfully to TMax (seems to quit around 2.36).
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      1. USDaniel Lichtblau
    2. COThank you! That certainly helped. Like you suggested, next I'll try to play around with NDSolve settings. Any suggestions?
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    3. COPreferably, you shouldn't use variables names starting with an uppercase letter as that may cause conflicts with built-in names (that all start with a capital letter). The line `TraditionalForm[EvapThickFilm[S, G, E1, K1, D1, VR, M, R]];` doesn't make sense. There is no assignment and the ; supresses any output. Hence there is no net effect.
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      1. USSjoerd C. de Vries
 

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