Heat equation solution with finite element method on uniform and random unidimensional mesh
fem1d: Solve the monodimensional heat equation rho*u_t - (cu_x)_x = f
with Dirichlet Dirichlet Conditions:
u(0) = alpha
u(1) = beta
or
with Dirichlet Neumann Conditions:
u(0) = alpha
c(1)u'(1) = beta
Input:
fem1d(N, meshname, bctype, bc, fname, cname, rhoname, dt, Tmax, integname, u0name, odename)
N -> Nodes Number
meshname -> Function name (without .m) containing the mesh - Uniform mesh, "muniform.m" - Quadratic mesh, "muquadratic.m" - Random mesh, "random.m"
bctype -> String, 'DD' or 'DN' selects the conditions type
bc -> Array holding the boundary conditions, two elements - Boundary Condition in 0 - Boundary Condition in 1
fname -> Function name (without .m) containing the f definition
cname -> Function name (without .m) containing the c definition
rhoname -> Function name (without .m) containing the rho definition
dt -> Time step
Tmax -> Max time
integname -> Function name (without .m) containing the numerical integration algorithm - Trapezoid method, "trapezoid.m" - Medium point method, "mediumpoint.m" - Simpson Method, "simpson.m"
u0name -> Function name (without .m) containing the initial data
odename -> Function name (without .m) containing the numerical ode solving algorithm - Esplicit Euler, "eulerEsplicit.m" - Implicit Euler, "eulerImplicit.m"