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Feb
2
revised Partial Differential Equation in Parallel
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Feb
2
revised Problems when solving a nonlinear PDE system with NDSolve
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Feb
1
revised Problems when solving a nonlinear PDE system with NDSolve
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Feb
1
comment Problems when solving a nonlinear PDE system with NDSolve
"Is there any offline version of such conversion tools", check this post:mathematica.stackexchange.com/q/1137/1871 . As to your new update, since I'm now at home and have no access to the new mentioned article, I'd like to stop verifying the model, I write this comment mainly to mention, the NDSolve::bcart: can be suppressed by using T[x, 0] == (Tw - Tgin) (Exp[1000 (x - xr)]) + Tgin instead of the corresponding boundary, NDSolve::pdord can be suppressed by using neweq5 = D[sys[[5]], t] /. Solve[D[sys[[4]], t], Derivative[0, 2][Tg][x, t]][[1]]; instead of eq5.
Jan
30
comment Problems when solving a nonlinear PDE system with NDSolve
BTW, I usually use steampiano.net/msc to convert the special characters. halirutan's extension is quite unstable at least in my Chrome.
Jan
30
comment Problems when solving a nonlinear PDE system with NDSolve
Then, you seemed to have eliminated eq7 in some way, and I think you haven't done it correctly, eq6 and eq7 should be something like eq6 = D[ρg*ϕb*yo2b[x, t], t] + D[ρg*yo2b[x, t]*ub*ϕb, x] + D[ρg*ϕb*yo2b[x, t]*Vo2b, x] == (-hm)*A3*(yo2b[x, t] - yo2s[x, t]); eq7 = D[ρgs*ϕs*yo2s[x, t], t] + D[ρgs*ϕs*yo2s[x, t]*Vo2s, x] == (-ωo)*no1 - ωa*no3*hm*A3*(yo2b[x, t] - yo2s[x, t]); . As to the article, to be honest I can't understand it very well, so long I can't tell how $c_p,c_{\text{pg}},d,D,u_b,V_{O_{2_b}},V_{O_{2_s}},\alpha ,\phi _b,\phi _s$ is calculated.
Jan
30
comment Problems when solving a nonlinear PDE system with NDSolve
And there're still mistakes, here are those I can identify: 1. ho = ho/1000; hp = hp/1000; ha = ha/1000; is redundant; 2. Ao = 569 10^6; Ap = 2 10^14; Aa = 5 10^5; 3. 10*D[yc[x, t], t] and 10*D[ya[x, t], t] should be D[ρ*yc[x, t], t] and D[ρ*ya[x, t], t] where ρ = (yc[x, t] + ya[x, t]) ρc + ρf (1 - yc[x, t] - ya[x, t]);; 4. The unknown functions should be {T, yc, ya, yo2s, yo2b, Tg}, according to the article. (u should probably be eliminated, there're 7 equations anyway. )
Jan
28
comment Constructing a particular Toeplitz matrix with a certain rule
@Student See my edit
Jan
28
revised Constructing a particular Toeplitz matrix with a certain rule
added 302 characters in body
Jan
28
comment Constructing a particular Toeplitz matrix with a certain rule
@Student You forgot to Clear[x]
Jan
28
answered Constructing a particular Toeplitz matrix with a certain rule
Jan
28
revised Implementation of a matrix formula
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Jan
28
revised Implementation of a matrix formula
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Jan
28
comment Implementation of a matrix formula
I'm afraid this isn't what OP is looking for……he's trying to implement the formula, rather than ploting the BSpline surface.
Jan
28
answered Implementation of a matrix formula
Jan
25
awarded  Necromancer
Jan
23
awarded  Necromancer
Jan
23
comment Solving Fredholm equation of the 2nd kind
It may be better to remove the option Method->NIntegrate, without it the calculation is much faster and the error with n=1000 is -0.000224447 - 0.0137966 I
Jan
23
comment Solving Fredholm equation of the 2nd kind
I don't think there's such guarantee… if you read the original paper, you will notice FredholmKind2 is essentially discretize the integral with quadrature rule (some improvement is introduced when Method -> NIntegrate is added, of course) and the precision of the result will be undoubtedly influenced by n. BTW, n = 50000 is way too large, n = 2500 is probably enough, I guess. And you can try modifying the line delta = deltaX /@ SI to delta = ParallelMap[deltaX, SI]
Jan
23
comment Solving Fredholm equation of the 2nd kind
Probably because n is not big enough. n=1000 produces 0.0010060712 - 0.0104718749 I.