Description

PARSEEQN Parse string equations and return eqn struct.

[ EQN ] = PARSEEQN( CEQN, CDVAR, CSDIM ) Parse string equation(s) and return weak finite element equation struct form and coefficients.

Input        Value/Type             Description
-----------------------------------------------------------------------------------
ceqn         cell array/string      Equation string or cell array of strings
cdvar        cell array/string      Dependent variable name(s)
csdim        cell array/string      Space dimension coordinate name(s)

String quations supports the following syntax

u@f$     - time derivative for u (@f$ = single quote)
u      - dependent variable u (explicit)
u_t    - dependent variable u (implicit)
ux     - space derivative for u in x-direction (explicit, rhs)
u_x    - space derivative for u in x-direction (implicit)
ux_t   - space derivative for u in x-direction (implicit)
ux_x   - 2nd space derivative for u in x-direction
(.)_t  - Multiplication of expression with test function
(.)_x  - Multiplication of expr. with test function in x-direction
(.)_tx - Multiplication of expr. with test function in x-direction

an underscore indicates multiplication with a test function, t, operating on the preceding expression. For expressions in parentheses with multiple dependent variable factors the operation is applied to the first from the reversed direction, for example (2*uy+u*ux)_x will be expanded to 2*uy_x+u*ux_x. Application of derivatives _x to constants, variables, or first of dependent variables will also change the equation sign accounting partial integration in the weak fem formulations. In addition expressions can be built up with standard MATLAB commands, functions, and operators such + - * / sqrt() log() etc. For elements supporting the curl operator a corresponding _c postfix is also supported.

Example

1) Poisson's equation in 1D

  seqn = 'da*u'' - (D*ux)_x = f';
  eqn  = parseeqn( seqn, 'u', 'x' );

  Gives, eqn.m: the mass matrix, in this case scaled by da

  eqn.m.form{:} >> [1;1]
  eqn.m.coef{:} >> da

  eqn.a: implicit bilinear form, here diffusion matrix scaled by D

  eqn.a.form{:} >> [2;2]
  eqn.a.coef{:} >> D

  eqn.f: linear right hand side source term

  eqn.f.form{:} >> 1
  eqn.f.coef{:} >> f

See also: expandeqn, assemblea, assemblef