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Feel free to correct the grammar mistakes in my posts.


Apr
2
comment Use de Casteljau algorithm to create Bezier Curve in Mathematica
Since I'm also not sure what OP is looking for, I'd like to leave this as a comment :) It's just a simplified version of your decasteljau: de[p_, t_] := Nest[MovingAverage[#, {1 - t, t}] &, p, Length@p - 1]
Apr
1
comment BVP system of nonlinear coupled ODEs
Then you'll have a hard time looking for a proper "StartingInitialConditions"……there're many examples for shooting method in this site, you can have a search.
Apr
1
comment How do you find the general solution to a higher order nonhomogeneous differential equation?
Have a look at the document of DSolve.
Mar
27
reviewed Approve suggested edit on Minimize: How to work with specific numeric types
Mar
27
comment How to find discretezation error of NDSolve
The last part (Spatial Error Estimates) of this tutorial may be helpful?
Mar
27
comment periodicity of a solution of ndsolve pde
In fact the solution is not periodic, just analyse the 1st b.c.: Tanh[t] isn't periodic at all, it's monotone increasing, so the b.c. isn't periodic, then how can the solution be periodic?
Mar
26
comment Trying to solve a differential equation with a piecewise initial condition
DSolve can't handle heat conduction equation, consider NDSolve instead if a numerical solution is OK, or you can refer to this post.
Mar
26
comment ExpToTrig transforms solution to 4th order ODE into unwanted form
How about HoldForm@Evaluate@DSolve[a y''''[x] + b*y[x] == 0, y[x], x] /. E^x_ :> (Cos[-I x] + I Sin[-I x]) ?
Mar
25
comment Do you really want to quit the kernel? Yes!
For a better understanding of the second solution, I think it's better to mention this answer :)
Mar
22
reviewed Approve suggested edit on Constructing election cartograms?
Mar
21
comment Shooting method problem
Your code contains simple mistakes. the third argument of NDSolve should be {x, 0, 10}. What's the meaning of Map here? The equation in your code is different from the one at beginning: is it u''[x] - u'[x]/x or u''[x] - u'[x]? Your i.c. is inconsistent with what you choose in your "StartingInitialConditions", is it u[0.001]==0 or u[0.001]==1? The x[t] in your Plot should be u[t]. After correcting all this, your code can easily give a result with no error.
Mar
17
comment How do I solve a PDE with a strange boundary condition?
@george2079 Wow, this time it seems to be true! If so, it'll be the best news for me about v10 :D
Mar
17
revised How do I solve a PDE with a strange boundary condition?
notice my misunderstanding for part of Ruebenko's code, so description revised.
Mar
16
revised How do I solve a PDE with a strange boundary condition?
correct some typos in the FEM formula
Mar
15
awarded  Necromancer
Mar
15
revised How do I solve a PDE with a strange boundary condition?
correct several typos
Mar
15
answered How do I solve a PDE with a strange boundary condition?
Mar
11
comment Shooting method for solving 3rd Oder ODE with RK method
Seems that since you add a - after my name, I didn't receive the message for your comment. I chose the initial condition y''[0] == 1 for I didn't notice it's just assumed and the actually boundary is f'[Infinity] == 1, then, if you want to apply shooting method, you may be interested in this and this post.
Mar
11
comment NDSolve_ODESolve_Plotsolution
Just as @Sektor said, that's because NDSolve is a numerical solver, so those parameters need numeric values. Oh, I just tried it and found your equation can be solved by DSolve: Clear[a, v, e]; eqn = (-v a^2/2) ψ''[x] - v Cos[2*Pi*x/a]*ψ[x] == e*ψ[x]; sol = DSolve[{eqn, ψ[0] == 0, ψ'[0] == 1}, ψ, x]. However, to get the plot you still need values for those parameters.
Mar
11
comment NDSolve_ODESolve_Plotsolution
Welcome to mathematica.SE! Then, your code is full of simple mistakes, you'd better make some effort on learning the basic syntax of Mathematica before using it. After removing those mistakes and add values for a, Subscript[V, 0] and E, the equation can be easily solved: a = 1; v = 1; e = 1; eqn = (-v a^2/2) ψ''[x] - v Cos[2*Pi*x/a]*ψ[x] == e*ψ[x]; sol = NDSolve[{eqn, ψ[0] == 0, ψ'[0] == 1}, ψ, {x, 10^-8, 1.005}]; Plot[ψ[x] /. sol, {x, 10^-8, 1.005}]. Also, you may be interested in this post.