CAJ | 학술논문

用线性方法对半线性抛物问题进行求解.方法依赖粗、细二重网格,针对粗解在细网格上的修正提出了两种算法,算法1是乘积倍的增长精度而算法2足平方倍的增长精度,而且重复算法1、2的最后几步可以任意阶地逼近细网格上的非线性解.数值算例验证了算法的可行性和有效性.
용선성방법대반선성포물문제진행구해.방법의뢰조、세이중망격,침대조해재세망격상적수정제출료량충산법,산법1시승적배적증장정도이산법2족평방배적증장정도,이차중복산법1、2적최후궤보가이임의계지핍근세망격상적비선성해.수치산례험증료산법적가행성화유효성.
Two efficient two-grid schemes are presented in this paper for the approximation of semilinear parabolic equations using the finite difference method. The proposed techniques are based on denning finite different schemes on a coarse grid and a fine grid respectively. By the two-grid algorithms, the semilinear parabolic problem is solved by linear method efficiently without sacrificing the order of accuracy on the fine grid solution. A remarkable fact is that any order accuracy of approximation in coarse grid size can be obtained if other iterations are performed similarly to last steps of the algorithms. Numerical examples show the feasibilities and properties of the algorithms are valid.