finite difference solution to multivariate, linear boundary problems

This function solves certain multivariate boundary value problems using finite difference method

This function finds approximate solution to boundary value problems
generated by a system of time-dependent,
linear, first order diferential equations
and linear boundary conditions
by using the finite difference method.
The general form of the problems adressed is
d(t) .* x'(t) + L(t) * x(t) = z(t)
b_i * x(t_i) = w_i for i=1,2,...,m

where

t is a variable (time)
x(t) is a column vector of m unknown functions x_1(t),...,x_m(t)
' means differentiation with respect to t
t_i and w_i (i=1,2,...,m) are known scalars
b_i (i=1,2,...,m) are known row vectors of size 1*m
d(t), c(t) and z(t) are t-dependent column vectors
L(t) is a t-dependent matrix of size m*m