Solving a Partial Differential Equation

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Thread starter YongL
Start date Apr 8, 2008
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Differential Differential equation Partial

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SUMMARY

The discussion focuses on solving the Laplace equation in cylindrical coordinates, specifically utilizing variable separation techniques. The equation is expressed as phi(x,y)=X(x)Y(y), where X''+X'/x+cX=0 represents a 0-order Bessel equation in x, and Y''-cY=0 in y. The constant 'c' is defined as an arbitrary positive or negative real constant. The solution method is confirmed effective by participant Roberto.

PREREQUISITES

Understanding of partial differential equations (PDEs)
Familiarity with cylindrical coordinate systems
Knowledge of Bessel functions and their properties
Experience with boundary value problems

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Study the derivation and applications of Bessel functions
Explore advanced techniques in solving partial differential equations
Learn about boundary conditions in cylindrical coordinates
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Mathematicians, physicists, and engineers involved in solving partial differential equations, particularly those working with cylindrical geometries and boundary value problems.

Apr 8, 2008

YongL

A partial differential equation.

Last edited: Apr 8, 2008

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Apr 8, 2008

Roberto Bramb

It is the Laplace equation in cylindrical coordinates with symmetry about y-axe.
You can solve it by variable separation, once given the boundary condition:
phi(x,y)=X(x)Y(y)

X''+X'/x+cX=0 (in x, 0-order Bessel equation)
Y''-cY=0 (in y)
c=arbitrary positive/negative real constant