Apparatus for numerical calculation of ordinary differential equations, method and program for computing ordinary differential equation in computer

摘要

Problem to be solved: to solve an ordinary differential equation mathematically modeled by numerical computation, and to execute the calculation of the steady differential equation of stiff.SolutionAn ordinary differential equation that includes a state variable vector term representing a state and an input vector term representing an input multiplied by first and second coefficient matrices, respectively;It has a form of difference equation for discrete time determined by a given calculation step.The first and second coefficient matrices are respectivelyApproximate matrix exponential functionsContains a first degree series of finite degree of magnitude consisting of a power law of the product of the predetermined calculation step and the constant matrixA state equation is set.The prime computation means 502 is a pre calculating meansThe computation step is separated into a time invariant time constant computation step hexp and time variable computation step h which can be changed in time.The ymmy matrix, which is the second matrix power series of finite degree, composed of the power terms of the product of the time invariant calculation step hexp and the constant matrix AThe first constant coefficient matrix and the second constant coefficient matrix based on the yummy matrix areIt is calculated beforehand in advance of the solution operation of the equation of state.The equation of state calculating means 509 calculates the first and second constant coefficient matrices calculated by the yummy matrix calculation means The arithmetic operation for the difference equation is executed while calculating the first coefficient matrix and the second coefficient matrix by the simple multiplication operation between the time variable calculation steps calculated by the pulse signal measuring means 508 sequentially.Even if the degree n of the matrix exponent approximation becomes longer, the power series can be calculated as a ymmy matrix in advance, so that the arithmetic operation of the equation of state can be performed with a high accuracy and a shorter computation time.Diagram