 Boundary lifting

Subtract a known function with the required boundary trace so that the remaining unknown has homogeneous boundary conditions. For an interval with Dirichlet boundary conditions $g(t),h(t)$, $\ell =(1-x/L)g+(x/L)h$ is a simple lifting. In $w_t=w_{xx}-cw$, $z=w-\ell$ has forcing $-{\ell }_t-c\ell$ and zero endpoint values. This improves Fourier sine series convergence.