Two ADI Methods For The Telegraph Equation

There are many non-linear developmental equations in the process of modern physics research. Telegraph equation which shows the relationship between voltage and current in well-proportioned transmission lines is deduced from the law of voltage and current changes in telegraph lines, therefore, the equation is also known as the transmission line equation. Due to its vital physical significance more and more experts and scholars pay increasingly close attention to it with the gradual in-depth understanding.First of all, there is an overview of the background and development status of telegraph equation and the method to solve the equation. Meanwhile, the basic theory of knowledge such as marks, concepts and lemmas is introduced in this paper as well.Moreover, to non-linear telegraph equation with initial boundary value problem, the methods of ADI structure finite differences method and ADI structure finite element method are widely adopted. The Alternating-Direction Schemes can turn multi-dimensional problem into a series of one-dimensional problem and iterative matrix of x, y are triple diagonal matrices which have same structure, so they are easy to computeand easy to pro-gram for parallel computing. At last some numerical results are presented to prove theory analysis.