Shifted-Legendre orthonormal method for high-dimensional heat conduction equations

In this paper, a numerical alogorthm for solving high-dimensional heat conduction equations is proposed. Based on Shifted-Legendre orthonormal polynomial and $\epsilon -$best approximate solution, we extend the algorithm from low-dimensional space to high-dimensional space, and prove the convergence of the algorithm. Compared with other numerical methods, the proposed algorithm has the advantages of easy expansion and high convergence order, and we prove that the algorithm has $\alpha$-Order convergence. The validity and accuracy of this method are verified by some numerical experiments.