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of converting to more equations. So let us load the package: Needs["PacletManager"] PacletInstall["CompoundMatrixMethod", "Site" -> "http://raw.githubusercontent.com/paclets/Repository/master … "] Needs["CompoundMatrixMethod"] Convert the system of ODEs into the matrix form, which gives all the matrices: sys = ToMatrixSystem[{eq1, eq2}, {bcs1, bcs2, matchconds}, {y,z}, {x, x1, x2, x3}, λ …
answered Aug 23 '18 by KraZug
$whose roots correspond to eigenvalues of the original problem, which I've just put on GitHub. Install the package via: Needs["PacletManager"] PacletInstall["CompoundMatrixMethod", "Site … ["CompoundMatrixMethod"] sys = ToMatrixSystem[y''[x] == - ω^2 y[x], {y[0] == 0, y[1] == 0}, y, {x, 0, 1}, ω] Now Evans[ω, sys] gives a function that can be evaluated at any complex$\omega$. Roots of this … answered Dec 7 '17 by KraZug notebook with examples), more details are in my other answers to questions here, and a good introduction to the method is in this pdf. Install and load the package: PacletInstall["CompoundMatrixMethod … ", "Site" -> "http://raw.githubusercontent.com/paclets/Repository/master"]; Needs["CompoundMatrixMethod"] First write the system in the form$\mathbf{y}' = \mathbf{A} \cdot \mathbf{y}$using the … answered Jul 13 by KraZug first time): Needs["PacletManager"] PacletInstall["CompoundMatrixMethod", "Site" -> "http://raw.githubusercontent.com/paclets/Repository/master"] Then we first need to turn the ODEs into a … matrix form$\mathbf{y}'=\mathbf{A} \cdot \mathbf{y}$, using my function ToMatrixSystem (note capital E is reserved, so use lower case here): Needs["CompoundMatrixMethod"] sys = ToMatrixSystem[-ψ … answered Apr 28 by KraZug ["CompoundMatrixMethod", "Site" -> "http://raw.githubusercontent.com/paclets/Repository/master"] Then we first need to turn the ODEs into a matrix form$\mathbf{y}'=\mathbf{A} \cdot \mathbf{y}$, using my … function ToMatrixSystem. Needs["CompoundMatrixMethod"] sys = ToMatrixSystem[-u''[x] + V[x] u[x] == e u[x], {u[-L] == 0, u[L] == 0}, {u}, {x, -L, L}, e] /. V -> Function[{x}, x^2] Now the … answered May 1 by KraZug partial explanation is at my previous question, and a good introduction to the method is in this pdf. You can install the package using: PacletInstall["CompoundMatrixMethod", "Site" -> "http … ://raw.githubusercontent.com/paclets/Repository/master"] First we'll load the package: Needs["CompoundMatrixMethod"] And then we define the differential equation and some boundary conditions … answered Mar 8 '18 by KraZug available at these two questions, or this PDF. Install the package (also available on my github page): Needs["PacletManager"] PacletInstall["CompoundMatrixMethod", "Site" -> "http … ://raw.githubusercontent.com/paclets/Repository/master"] Load the package and setup the system: Needs["CompoundMatrixMethod"] sys = ToMatrixSystem[f''[x] == λ x f[x], {f[-1] == 0, f[0] == 0}, f, {x, -1, 0}, λ … answered Oct 5 '18 by KraZug ["CompoundMatrixMethod", "Site" -> "http://raw.githubusercontent.com/paclets/Repository/master"] Then we first need to turn the ODEs into a matrix form$\mathbf{y}'=\mathbf{A} \cdot \mathbf{y}$, using my function … ToMatrixSystem: Needs["CompoundMatrixMethod"] m = 3; q = 4/3; op = -(1 - ζ^2) u''[ζ] + ζ u'[ζ] + 2 q (2 ζ^2 - 1) u[ζ]; sys[ζend_] = ToMatrixSystem[op == a u[ζ], {u[0] == 0, u[ζend] == 0}, u, {ζ, 0 … answered Apr 24 by KraZug or the github for some more details. First we install the package (only need to do this the first time): Needs["PacletManager"] PacletInstall["CompoundMatrixMethod", "Site" -> "http … ["CompoundMatrixMethod"] pars = Rationalize[{L -> 6.9, A -> 0.0133, a0 -> 410, c1a -> 0.003, c2a -> 0.002, c1p -> -2.5 10^-6, c2p -> 4.3 10^-6}]; eqns = {-(a0^2/A) D[ϕ2[xi], xi] == λ ϕ1[xi], -A D[ϕ1[xi], xi … answered Apr 23 by KraZug 0answers magical package in one of the answers in here: Needs["PacletManager"] PacletInstall["CompoundMatrixMethod", "Site" -> "http://raw.githubusercontent.com/paclets/Repository/master"]; Needs … ["CompoundMatrixMethod"] f = 1 - 2*(M/r); V = f*(l*((l - 1)/r^2) + (2*(1 - S^2)*M)/r^3); M = 1; l = 2; S = 2; sys = ToMatrixSystem[f*D[f*D[\[Chi][r], r], r] - V*\[Chi][r] == \[Omega]*\[Chi][r], {\[Chi][3 … asked Jul 2 by Edison Cesar ["PacletManager"] PacletInstall["CompoundMatrixMethod", "Site" -> "http://raw.githubusercontent.com/paclets/Repository/master"] Then we first need to turn the ODEs into a matrix form$\mathbf{y … fix, or at least error gracefully): Needs["CompoundMatrixMethod"] subs = {γ -> 1.67, ϵ -> 0.01, d -> 0.05, H -> 1.1, gpar -> Function[{x}, 0.38], ρ0 -> Function[{x}, Exp[-x/H]], p0 …
questions or the github for some more details. First we install the package (only need to do this the first time): Needs["PacletManager"] PacletInstall["CompoundMatrixMethod", "Site" -> "http … ["CompoundMatrixMethod"] sys = ToMatrixSystem[{λ F'''[x] - 2 λ β F''[x] + ((λ β - 1) β - μ) F'[x] + β^2 F[x] == 0}, {F[0] == 0, F''[0] == β F'[0], F''[1] == β F'[1]}, F, {x, 0, 1}, μ] The object sys …
Update: This implementation is now a package called CompoundMatrixMethod, hosted on github. It can be installed easily by evaluating: Needs["PacletManager"] PacletInstall["CompoundMatrixMethod
package, CompoundMatrixMethod, which is available on my github page or can be installed via the PacletServer: Needs["PacletManager"] PacletInstall["CompoundMatrixMethod", "Site" -> "http … ://raw.githubusercontent.com/paclets/Repository/master"] Load the package and copy the code from the question: Needs["CompoundMatrixMethod"] f = 20; b = 2; eps0 = 1*^-10; l = -2; R = 2; Rcutoff …
", \ "CloudExpressionLoader", "CloudObject", "CloudObjectLoader", \ "CodeSeal", "CodeSealAuthoring", "CompiledFunctionTools", \ "CompoundMatrixMethod", "CoursewareTools", "CrossRef", \ "CrossRefLoad …