## Structural Optimization of One-dimensional Poisson Equation and Its Exact Solution to PDEs

**ZHANG Xiu-ying;Zhengzhou Railway Vocational & Technical College;**

The exact solution of PDEs is difficult in practice. Taking one-dimensional Poisson equation as an example, the symmetry of the equation is analyzed by Wu method, and the optimal structure of the equation is designed. The optimal transposition and adjoint operators of one-dimensional Poisson equation are obtained by two definitions, thus the structure of the equation is optimized step by step. On this basis, the exact solution of PDEs for single element of optimal structure of one-dimensional Poisson equation is calculated by invariant method. Under two classical symmetry conditions, two new solutions for PDEs are obtained respectively. This result is a new attempt to solve PDEs precisely.

【Fund】：
2017年度河南省高等教育教学改革研究与实践项目(2017SJGLX570);;
2018年度河南省高等学校重点科研项目计划(19B880029)

【CateGory Index】： O175.2

【CateGory Index】： O175.2

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