Boundary lifting
= Boundary lifting
{title2=$w=\ell+z$}
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.