分片近似法求解数学物理方程反问题

he limitation of inversion method that based on optimization theory is pointed out. The advantage and disadvantage of direct method is analized. In oder to cover the shortage of the direct methods, a new method---partitioned approximating method of solving the indirect problems of mathematical physics equation is proposed after borrowing ideas from finite element method and making use of double difference criterion’s merits. The priciples of the method and the key problems (approximating function’s convergence and computation time of dertermining the coefficient) that need to solve is discussed. The corresponding countermeasure is presented: adopt partitioned approximation to avoid the computing dificulty and adopt double difference criterion to avoid the approximating function’s diverging. Then an example of ordinary differential equation’s inversion is listed to instruct the constructing process and solving process of the method. Compared to the inversin method that based on optimization theory, the proposed method of this paper does not need to solve the differential equation of the inverse problem and does not need the parameter’s pilot calculation and the parameter that need to inverse can be got by once-through calculation. The numerical experiment’s results indicate the proposed method’s precision and validity.