Re: matching conditions in PDE
- To: mathgroup at smc.vnet.net
- Subject: [mg42179] Re: [mg42155] matching conditions in PDE
- From: CAP F <Ferdinand.Cap at eunet.at>
- Date: Sat, 21 Jun 2003 20:56:58 -0400 (EDT)
- References: <200306210649.CAA13186@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Vladimir Petrov wrote: > Hi, > > I would like to know how to solve numerically a partial > differential equation (the heat equation) in a medium > consisting of two subregions characterized by different > physical parameters. How to set in NDSolve the matching > conditions at the boundary between the two subregions ? > Could you give an example. > Thank you. > Regards > > Vladimir Mathematical Methods of Physics and Engineering with Mathematica Ferdinand F . Cap, CRC-Press/Chapman and Hall, 2003, ISBN 1584884029, 56 Codes to be downloaded from www.crcpress.com 1 Introduction 1.1 What is a boundary problem? 1.2 Classification of partial differential equations 1.3 Types of boundary conditions and the collocation method 1.4 Differential equations as models for nature 2 Boundary problems of ordinary differential equations 2.1 Linear differential equations 2.2 Solving linear differential equations 2.3 Differential equations of physics and engineering 2.4 Boundary value problems and eigenvalues 2.5 Boundary value problem as initial value problem 2.6 Nonlinear ordinary differential equations 2.7 Solutions of nonlinear differential equations 3 Partial differential equations 3.1 Coordinate systems and separability 3.2 Other methods to reduce partial to ordinary differential equations 3.3 The method of characteristics 3.4 Nonlinear partial differential equations 4 Boundary problems with one closed boundary defined by coordinate lines 4.1 Laplace and Poisson equation 4.2 Conformal mapping in two and three dimensions 4.3 D'Alembert wave equation and string vibrations 4.4 Helmholtz equation and membrane vibrations 4.5 Rods and the plate equation 4.6 Approximation methods 4.7 Variational calculus 4.8 Collocation methods 5 Boundary problems with two closed boundaries 5.1 Inseparable problems 5.2 Holes in the domain.Two boundaries belonging to different coordinate systems 5.3 Corners in the boundary 6 Nonlinear boundary problems 6.1 Some definitions and examples 6.2 Moving and free boundaries 6.3 Waves of large amplitudes. Solitons 6.4 Rupture of an embankment-type dam 6.5 Gas flow in a combustion engine List of codes (1 - 56) see: www.crcpress.com/downloads (F.Cap, Mathematical Methods in Physics and Engineering with Mathematica, ccrcpress and Chapman and Hall, 2003, ISBN 1584884029 c1 Equation of motion of a parachutist c2 Differentiate and integrate c3 The differential equation describing the spread of an epidemic disease c4 The Wronskian of exp(x), exp(2x) c5 The most general linear differential equation of second order c6 Inhomogeneous equation of oscillations c7 An initial value problem c8 Homogeneous boundary value problem c9 Inhomogeneous boundary value problem c10 Pick out values of a numerical solution of a problem with varying boundary values c11 Preparing the shooting method for inhomogeneous boundary value problems c12 Series expansion of a Lie-series solution c13 Learn a loop for the shooting method c14 Limit cycle of the Van der Pol equation c15 High voltage electrostatic parametric generator US patent c16 Phase portrait of the Duffing equation c17 Phase portrait Mathieu equation c18 Phase portrait of the pendulum equation c19 Jacobian matrix of spherical coordinates c20 Vector analysis: curl in spherical coordinates c21 Separation setup for the Laplacian c22 Laplace transformation c23 Characteristics of one-dimensional flow (3.3.27), see page 119 of the book c24 Solution of the heat conduction equation using a similarity transformation c25 Harmonic polynomials as solution of the Laplacian c26 Biharmonic polynomials solve the static homogeneous plate equation c27 Generalized Bessel and Kummer equations c28 Whittaker, Gegenbauer and Weber equation c29 Legendre equation with Rodriguez formula c30 Laguerre equation with Rodriguez formula c31 Hermite equation with Rodriguez formula c32 Vector field - cover of the book c33 Conformal mapping c34 2D flow around a cylinder c35 Solution of the damped Helmholtz equation c36 Free bending vibrations of a rod c37 Two boundaries for the Laplace equation c38 Inhomogeneous boundary problem for the Laplace equation c39 Nontrivial homogeneous boundary problem of the Laplace equation c40 COLLOC, a FORTRAN PROGRAM to calculate the eigenvalues of a circular membrane in CARTESIAN COORDINATES c41 Eigenvalue problem for a circular membrane. Calculation in cartesian coordinates c42 Clamped Cassini membrane in cartesian coordinates c43 Circular membrane with varying surface mass density. Includes four-fold loop c44 Circular plate with two homogeneous boundary conditions c45 Laplace equation in polar coordinates with a singularity c46 Laplace equation with two different boundaries, inner inhomogeneous on a square and outer homogeneous on circle c47 Membrane with an homogeneous boundary condition on an inner circle and an inhomogeneous outer boundary condition c48 Corner in a boundary curve c49 Steepening up of a large-amplitude wave c50 Envelope soliton c51 Laplace equation with outer inhomogeneous boundary values on square and inner homogeneous boundary values on circle c52 Gaussian elimination c53 The shooting method c54 Navier solutions of the plate equation c55 From Maxwell's to vector Helmholtz equations c56 Toroidal wave guides
- References:
- matching conditions in PDE
- From: Vladimir Petrov <voldemar1@front.ru>
- matching conditions in PDE