The Crank-Nicolson Hermite Cubic Orthogonal Spline Collocation Method for the Heat Equation with Nonlocal Boundary Conditions (Advances in Applied Mathematics and Mechanics, 2021)
We formulate and analyze the Crank-NicolsonHermite cubic orthogonal spline collocationmethod for the solution ofthe heat equation in one space variablewith nonlocal boundary conditions involving integrals ofthe unknown solution over the spatial interval.Using an extensionof the analysis of Douglas and Dupont [23]for Dirichlet boundary conditions,we derive optimal order errorestimates in the discrete maximum norm in timeand the continuous maximum norm in space.We discuss the solution of the linear system arising at each time levelvia the capacitance matrix technique and the package COLROWfor solving almost block diagonal linear systems.We present numerical examples that confirm the theoreticalglobal error estimates and exhibit superconvergence phenomena.