The Numerical Solution Of Cardiac Electrophysiology Modelbythe Wavelet-Difference Method

The purpose of this dissertation is to develop a new method to solve theaction potential of cardiac electrophysiology model. The new method is combinedthe wavelet method with difference scheme. To solve the complex domain problem,difference scheme is used for the current item while wavelet interpolation for thediffusion item on a fictitious domain.Firstly，fictitious domain is applied to simplify the complicated boundaryproblem. Error estimate is obtained for half discrete scheme of TNNP model whichhas Neumann boundary value conditions.Secondly, this dissertation gives a wavelet method to solve a multi-dimensional reaction-diffusion equation. The numerical experiment of a simpleexample, which is similar with TNNP model, shows a higher precision and largertime steps than classical finite difference method with fixed space steps.Finally, the wavelet-difference scheme on fictitious domain is given to solvethe TNNP model. Choose forward-difference method for the current itemcontrolled by multigroup of differential equations, wavelet interpolation forsecond-order partial derivative items of spatial variables, and differential quotientfor the time partial derivative. Simulating the conduction process of actionpotential by applying stimulations on differnet positions of heart tissue, theexperimental results show that this numerical method is efficient.