Burgers方程混合问题的Lagrange插值逼近

Lagrange Interpolation Approximation of Mixed Problem of Burgers Equation

摘要: 利用等距节点为插值节点，构造Burgers方程混合问题的时空二元Lagrange插值逼近格式。即在时间和空间方向都采用Lagrange插值多项式进行逼近，化为非线性方程组，利用迭代方法进行求解。最后通过数值结果证明了算法内容的正确性与实用性，为研究其他问题提供了强有力的工具。

Abstract: The spatiotemporal binary Lagrange interpolation approximation scheme for the mixed problem of Burgers equation is constructed by using equidistant nodes as interpolation nodes. That is, La-grange interpolation polynomials are used to approximate in time and space, which are trans-formed into nonlinear equations and solved by fixed point iterative method. Finally, the numerical results prove the correctness and practicability of the algorithm, which provides a powerful tool for studying other problems.