Numerical algorithm for parabolic problems with non-classical conditions (Q2390023)

The authors consider the 1D heat equation with constant coefficients subject to initial conditions and nonlocal boundary conditions \[ \lambda_iu(i,t)+\gamma_iu_x(i,t)=\int_0^1 p_i(x)u(x,t)\,dx+q_i(t) \text{ for } i \in \{0,1\}. \] The numerical method is based on the truncation of a uniformly convergent series of the solution, which is assumed to lie in some reproducing kernel spaces. Numerical examples are provided.