摘要
利用有限差分法,给出了数值求解一类非线性偏微分方程的算法,并分析了算法的稳定性.考虑推广的热方程φ/t=2f(φ)/x2(特别是f为各项次数都为奇数的多项式函数),用Richtmyer线性化方法把向前差分所得的非线性方程组转化为线性方程组,再用经典的数值解法计算得到结果,最后由热方程数值解法的稳定性分析,证明了算法在函数为奇数次的单项式时的稳定性.
By using the finite difference method, an algorithm to solve a certain nonlinear partial differential e-quation numerically is given, and the stability of the algorithm is discussed. Precisely, we consider the gener- alizing heat equation φ2t = 32f（φ） x2 （especially, f is a polynomial with only odd - order terms）. By u-sing Richtmyer＇ s linearized method, we reduce the system of nonlinear equations obtained by forward differ-ence method to the system of linear equations. Then we got the solution by the classical numerical algorithm. Finally, similarly to the numerical algorithm for heat equation, we proved the stability of our algorithm for the monomial with odd order.
出处
《河南城建学院学报》
CAS
2013年第1期80-84,共5页
Journal of Henan University of Urban Construction
关键词
非线性偏微分方程
数值解
算法
稳定性
nonlinear partial differential equation
heat equation
numerical solution
algorithm
stability
