ider

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Hello everybody,

i am trying to use PDEchangecoords to transform a system of differential equations from Cartesian coordinates to toroidal coordinates. However, when i use a user defined coordinate transform from toroidal to Cartesian, i don't get the initial equations. Please find attached a minimal working environment.

i would highly appreciate your hints and suggestions!

Thank you

Best regards,

F

question.mw
 

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restart; with(DEtools); addcoords(invToroidal, [xi, eta, phi], [sinh(xi)*cos(phi)/(cosh(xi)-cos(eta)), sinh(xi)*sin(phi)/(cosh(xi)-cos(eta)), sin(eta)/(cosh(xi)-cos(eta))]); PDEchangecoords(diff(f(x, y, z), z), [x, y, z], toroidal, [xi, eta, phi]); PDEchangecoords(%, [xi, eta, phi], invToroidal, [x, y, z]); print("i would expect here to get", diff(f(x, y, z), z))

"i would expect here to get", diff(f(x, y, z), z)

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Hello everybody,

While i was trying to work on a physical math problem, a system of 4 integral equations is obtained. The right hand sides of these equations are known functions of r. The left hand sides contain double integrals with respect to lambda and t. i believe that an analytical determination of the 4 unknown functions f_1(t), f_2(t), f_3(t), and f_4(t) is far from being trivial, thus recourse to a numerical technique is necessary and indispensable.

 

i tried to express the unknown functions as series expansions in t and solve the resulting linear system of equations for the expansion coefficients, but unfortunately the coefficients are very large and the solution is strongly dependent on the number of coefficients. i was wondering whether someone here has some experience with such integral problems and is willing to assist and help. Any hint is highly appreciated.

 

i attach a Maple script including the equations.

Thank you,

 

>>>>>> Question.mw

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