Revisions to Replacing variable in an equation with an Interpolating function polynomial and plotting residual

deleted 90 characters in body

Source Link

edited Mar 21, 2018 at 12:00

9.3k
5
40
97

I think you are making a silly mistake by considering solution as a List when you have defined it as a InterpolatingFunction object. Here is little modification which may help

Clear[Eq0, FilmEqn, h, Bo, \[Epsilon]ϵ, K1, \[Delta]δ, Bi, m, r]
Eq0[h_, {Bo_, \[Epsilon]_ϵ_, K1_, \[Delta]_δ_, Bi_, m_, r_}] := \!\(
\*SubscriptBox[\(\[PartialD]\∂\), \(t\)]h\) + 
Div[-h^3 Bo Grad[h] + 
 h^3 Grad[Laplacian[h]] + (\[Delta]δ h^3)/(Bi h + K1)^3 Grad[h] + 
 m (h/(K1 + Bi h))^2 Grad[h]] + \[Epsilon]ϵ/(
Bi h + K1) + (r) D[D[(h^2/(K1 + Bi h)), x] h^3, x];
SetCoordinates[Cartesian[x, y, z]];
FilmEqn[Bo_, \[Epsilon]_ϵ_, K1_, \[Delta]_δ_, Bi_, m_, r_, time_] := 
Eq0[solution[x, y, time], {Bo, \[Epsilon]ϵ, K1, \[Delta]δ, Bi, m, r}]
expr = FilmEqn[0, 10^-6, 1, 10^-3, 1, 0.05, 0, time];
fun[a_, b_, t_] := Evaluate[expr /. x -> a /. y -> b /. time -> t];
Plot3D[fun[x, y, 100000], {x, 0, L}, {y, 0, L}, PlotPoints -> 40,Mesh ->None,
ColorFunction -> Hue, PlotRange -> All]

enter image description here

Plot3D[(fun[x, y, #] - fun[x, y, # - 1]), {x, 0, L}, {y, 0, L}, 
PerformanceGoal -> "Quality", 
Mesh -> None, ColorFunction -> Hue, 
PlotLabel -> "eq(t)-eq(t-1) at t:= " <> ToString[#]] &

enter image description here

I think you are making a silly mistake by considering solution as a List when you have defined it as a InterpolatingFunction object. Here is little modification which may help

Clear[Eq0, FilmEqn, h, Bo, \[Epsilon], K1, \[Delta], Bi, m, r]
Eq0[h_, {Bo_, \[Epsilon]_, K1_, \[Delta]_, Bi_, m_, r_}] := \!\(
\*SubscriptBox[\(\[PartialD]\), \(t\)]h\) + 
Div[-h^3 Bo Grad[h] + 
 h^3 Grad[Laplacian[h]] + (\[Delta] h^3)/(Bi h + K1)^3 Grad[h] + 
 m (h/(K1 + Bi h))^2 Grad[h]] + \[Epsilon]/(
Bi h + K1) + (r) D[D[(h^2/(K1 + Bi h)), x] h^3, x];
SetCoordinates[Cartesian[x, y, z]];
FilmEqn[Bo_, \[Epsilon]_, K1_, \[Delta]_, Bi_, m_, r_, time_] := 
Eq0[solution[x, y, time], {Bo, \[Epsilon], K1, \[Delta], Bi, m, r}]
expr = FilmEqn[0, 10^-6, 1, 10^-3, 1, 0.05, 0, time];
fun[a_, b_, t_] := Evaluate[expr /. x -> a /. y -> b /. time -> t];
Plot3D[fun[x, y, 100000], {x, 0, L}, {y, 0, L}, PlotPoints -> 40,Mesh ->None,
ColorFunction -> Hue, PlotRange -> All]

enter image description here

Plot3D[(fun[x, y, #] - fun[x, y, # - 1]), {x, 0, L}, {y, 0, L}, 
PerformanceGoal -> "Quality", 
Mesh -> None, ColorFunction -> Hue, 
PlotLabel -> "eq(t)-eq(t-1) at t:= " <> ToString[#]] &

enter image description here

I think you are making a silly mistake by considering solution as a List when you have defined it as a InterpolatingFunction object. Here is little modification which may help

Clear[Eq0, FilmEqn, h, Bo, ϵ, K1, δ, Bi, m, r]
Eq0[h_, {Bo_, ϵ_, K1_, δ_, Bi_, m_, r_}] := \!\(
\*SubscriptBox[\(∂\), \(t\)]h\) + 
Div[-h^3 Bo Grad[h] + 
 h^3 Grad[Laplacian[h]] + (δ h^3)/(Bi h + K1)^3 Grad[h] + 
 m (h/(K1 + Bi h))^2 Grad[h]] + ϵ/(
Bi h + K1) + (r) D[D[(h^2/(K1 + Bi h)), x] h^3, x];
SetCoordinates[Cartesian[x, y, z]];
FilmEqn[Bo_, ϵ_, K1_, δ_, Bi_, m_, r_, time_] := 
Eq0[solution[x, y, time], {Bo, ϵ, K1, δ, Bi, m, r}]
expr = FilmEqn[0, 10^-6, 1, 10^-3, 1, 0.05, 0, time];
fun[a_, b_, t_] := Evaluate[expr /. x -> a /. y -> b /. time -> t];
Plot3D[fun[x, y, 100000], {x, 0, L}, {y, 0, L}, PlotPoints -> 40,Mesh ->None,
ColorFunction -> Hue, PlotRange -> All]

enter image description here

Plot3D[(fun[x, y, #] - fun[x, y, # - 1]), {x, 0, L}, {y, 0, L}, 
PerformanceGoal -> "Quality", 
Mesh -> None, ColorFunction -> Hue, 
PlotLabel -> "eq(t)-eq(t-1) at t:= " <> ToString[#]] &

enter image description here

added 289 characters in body

Source Link

edited Sep 24, 2012 at 20:15

PlatoManiac

14.9k
2
43
75

I think you are making a silly mistake by considering solution as a List when you have defined it as a InterpolatingFunction object. Here is little modification which may help

Clear[Eq0, FilmEqn, h, Bo, \[Epsilon], K1, \[Delta], Bi, m, r]
Eq0[h_, {Bo_, \[Epsilon]_, K1_, \[Delta]_, Bi_, m_, r_}] := \!\(
\*SubscriptBox[\(\[PartialD]\), \(t\)]h\) + 
Div[-h^3 Bo Grad[h] + 
 h^3 Grad[Laplacian[h]] + (\[Delta] h^3)/(Bi h + K1)^3 Grad[h] + 
 m (h/(K1 + Bi h))^2 Grad[h]] + \[Epsilon]/(
Bi h + K1) + (r) D[D[(h^2/(K1 + Bi h)), x] h^3, x];
SetCoordinates[Cartesian[x, y, z]];
FilmEqn[Bo_, \[Epsilon]_, K1_, \[Delta]_, Bi_, m_, r_, time_] := 
Eq0[solution[x, y, time], {Bo, \[Epsilon], K1, \[Delta], Bi, m, r}]
expr = FilmEqn[0, 10^-6, 1, 10^-3, 1, 0.05, 0, time];
fun[a_, b_, t_] := Evaluate[expr /. x -> a /. y -> b /. time -> t];
Plot3D[fun[x, y, 100000], {x, 0, L}, {y, 0, L}, PlotPoints -> 40,Mesh ->None,
ColorFunction -> Hue, PlotRange -> All]

enter image description here

Plot3D[(fun[x, y, #] - fun[x, y, # - 1]), {x, 0, L}, {y, 0, L}, 
PerformanceGoal -> "Quality", 
Mesh -> None, ColorFunction -> Hue, 
PlotLabel -> "eq(t)-eq(t-1) at t:= " <> ToString[#]] &

enter image description here

I think you are making a silly mistake by considering solution as a List when you have defined it as a InterpolatingFunction object. Here is little modification which may help

Clear[Eq0, FilmEqn, h, Bo, \[Epsilon], K1, \[Delta], Bi, m, r]
Eq0[h_, {Bo_, \[Epsilon]_, K1_, \[Delta]_, Bi_, m_, r_}] := \!\(
\*SubscriptBox[\(\[PartialD]\), \(t\)]h\) + 
Div[-h^3 Bo Grad[h] + 
 h^3 Grad[Laplacian[h]] + (\[Delta] h^3)/(Bi h + K1)^3 Grad[h] + 
 m (h/(K1 + Bi h))^2 Grad[h]] + \[Epsilon]/(
Bi h + K1) + (r) D[D[(h^2/(K1 + Bi h)), x] h^3, x];
SetCoordinates[Cartesian[x, y, z]];
FilmEqn[Bo_, \[Epsilon]_, K1_, \[Delta]_, Bi_, m_, r_, time_] := 
Eq0[solution[x, y, time], {Bo, \[Epsilon], K1, \[Delta], Bi, m, r}]
expr = FilmEqn[0, 10^-6, 1, 10^-3, 1, 0.05, 0, time];
fun[a_, b_, t_] := Evaluate[expr /. x -> a /. y -> b /. time -> t];
Plot3D[fun[x, y, 100000], {x, 0, L}, {y, 0, L}, PlotPoints -> 40,Mesh ->None,
ColorFunction -> Hue, PlotRange -> All]

enter image description here

I think you are making a silly mistake by considering solution as a List when you have defined it as a InterpolatingFunction object. Here is little modification which may help

Clear[Eq0, FilmEqn, h, Bo, \[Epsilon], K1, \[Delta], Bi, m, r]
Eq0[h_, {Bo_, \[Epsilon]_, K1_, \[Delta]_, Bi_, m_, r_}] := \!\(
\*SubscriptBox[\(\[PartialD]\), \(t\)]h\) + 
Div[-h^3 Bo Grad[h] + 
 h^3 Grad[Laplacian[h]] + (\[Delta] h^3)/(Bi h + K1)^3 Grad[h] + 
 m (h/(K1 + Bi h))^2 Grad[h]] + \[Epsilon]/(
Bi h + K1) + (r) D[D[(h^2/(K1 + Bi h)), x] h^3, x];
SetCoordinates[Cartesian[x, y, z]];
FilmEqn[Bo_, \[Epsilon]_, K1_, \[Delta]_, Bi_, m_, r_, time_] := 
Eq0[solution[x, y, time], {Bo, \[Epsilon], K1, \[Delta], Bi, m, r}]
expr = FilmEqn[0, 10^-6, 1, 10^-3, 1, 0.05, 0, time];
fun[a_, b_, t_] := Evaluate[expr /. x -> a /. y -> b /. time -> t];
Plot3D[fun[x, y, 100000], {x, 0, L}, {y, 0, L}, PlotPoints -> 40,Mesh ->None,
ColorFunction -> Hue, PlotRange -> All]

enter image description here

Plot3D[(fun[x, y, #] - fun[x, y, # - 1]), {x, 0, L}, {y, 0, L}, 
PerformanceGoal -> "Quality", 
Mesh -> None, ColorFunction -> Hue, 
PlotLabel -> "eq(t)-eq(t-1) at t:= " <> ToString[#]] &

enter image description here

Source Link

created Sep 24, 2012 at 18:34

PlatoManiac

14.9k
2
43
75

I think you are making a silly mistake by considering solution as a List when you have defined it as a InterpolatingFunction object. Here is little modification which may help

Clear[Eq0, FilmEqn, h, Bo, \[Epsilon], K1, \[Delta], Bi, m, r]
Eq0[h_, {Bo_, \[Epsilon]_, K1_, \[Delta]_, Bi_, m_, r_}] := \!\(
\*SubscriptBox[\(\[PartialD]\), \(t\)]h\) + 
Div[-h^3 Bo Grad[h] + 
 h^3 Grad[Laplacian[h]] + (\[Delta] h^3)/(Bi h + K1)^3 Grad[h] + 
 m (h/(K1 + Bi h))^2 Grad[h]] + \[Epsilon]/(
Bi h + K1) + (r) D[D[(h^2/(K1 + Bi h)), x] h^3, x];
SetCoordinates[Cartesian[x, y, z]];
FilmEqn[Bo_, \[Epsilon]_, K1_, \[Delta]_, Bi_, m_, r_, time_] := 
Eq0[solution[x, y, time], {Bo, \[Epsilon], K1, \[Delta], Bi, m, r}]
expr = FilmEqn[0, 10^-6, 1, 10^-3, 1, 0.05, 0, time];
fun[a_, b_, t_] := Evaluate[expr /. x -> a /. y -> b /. time -> t];
Plot3D[fun[x, y, 100000], {x, 0, L}, {y, 0, L}, PlotPoints -> 40,Mesh ->None,
ColorFunction -> Hue, PlotRange -> All]

enter image description here

Stack Exchange Network

Return to Answer