变分迭代法在多维抛物型方程反问题中的应用

Application of Variational Iteration Method to Multi-dimensional Parabolic Inverse Problems

通过抛物型方程反问题:ut=Δu+p(t)u+(x,t),x∈,Ωt∈(0,T),ΩRn的求解,阐述了变分迭代法在多维抛物型方程中的应用原理,变分迭代法在二维、三维抛物型方程的应用充分显示了对求一系列精确解具有很快的收敛速度,变分迭代法的应用范围更加广泛.

This paper discusses the applying principle of variational iteration method to multi-dimensional parabolic equation based on the solution to the parabolic equation inverse problem： ut=Δu＋p（t）u＋（x,t）,x∈,Ωt∈（0,T）,ΩRn. The applications of variational iteration method to two-dimensional and three-dimensional parabolic equations show that the method is able to work out a series of exact solutions with a quick convergence rate, indicating that the method can be widely used.