Compact difference schemes for inhomogeneous boundary value problems.

In this paper, we investigate the method of the numerical solution of boundary value problems in inhomogeneous domains composed of homogeneous multidimensional parallelepipeds. The method is the symbiosis of high-order difference schemes in homogeneous subdomains and multipoint one-dimensional boundary conditions at interfaces. Due to splitting, the boundary value problem reduces to systems of linear algebraic equations with matrices different from a tridiagonal matrix by the availability of separate 'long' rows with more than three nonzero elements. Two algorithms are investigated to solve these systems. The first algorithm is based on the immediate transformation of the system of equations to a tridiagonal form. The second one is a generalization of the known sweep parallelizing method. [ABSTRACT FROM AUTHOR]