Method of undetermined function for finding special solution to poisson equation 方程特解的待定函数解法
The form solution to the mixed problem of one dimension inhomogeneous diffusion equation was given through the method of undetermined function 摘要利用待定函数法给出了一维非齐次扩散方程混合问题的形式解。
When solving the problems , we use the support vector regression ( svr ) . first assuming the formula of function , then according to the differential and boundary conditions we transform the original problem to the quadratic programming problem . finally , use the learning algorithm of svr to decide the parameters 只要事先假设出所求函数的表达式,然后根据已知的微分关系和边界条件对待求函数进行约束将原问题转化为二次规划问题,再采用支持向量机回归算法对样本进行学习即可求出参数,确定待定函数的关系式。
A summary of the main conclusions of our researches is in the following : ( 1 ) nonlinear partial differential equation ( npde ) is converted into an ordinary differential equation ( ode ) via a new anstaz . using undetermined function method , the exact solutions and solitary solutions of the npde are obtained by solving the ode 本文针对几个非线性发展方程,做了以下几点工作: ( 1 )通过一种新的变换将一类非线性偏微分方程化为常微分方程,然后用待定函数法求解常微分方程,得到非线性偏微分方程的精确解和孤立波解。