Abstract: Elements of a vector sequence A·&phgr;m are sampled to be stored in a memory. In this sampling, a combination of spatial sampling and local sampling on the basis of physical phenomenon is employed. A residual minimization coefficient &agr;1m (wherein l=1, . . . , L) used for obtaining a corrected approximate value &phgr;m is approximately obtained by using elements of a vector sequence A·&phgr;k (wherein k=m−L+1, . . . , m−1) stored in the memory.

Abstract: A·U+B(U)=f, wherein A is a linear differential operator, B is a nonlinear differential operator, and f is an inhomogeneous term (source term) in a nonlinear partial differential equation to be satisfied by a physical quantity U, is solved by successive approximation. In calculation, (f−A·Um−B(Um)) is given as a nonlinear residual rr of an approximate solution Um, wherein m is the number of repeating times, and the approximate solution Um is repeatedly corrected so as to reduce a norm of a nonlinear residual rm+1 employed in a subsequent step.