## Adaptive wavelet precise integration method for nonlinear Black-Scholes model based on variational iteration method.(English)Zbl 1275.65072

Summary: An adaptive wavelet precise integration method based on the variational iteration method (VIM) for the Black-Scholes model is proposed. The Black-Scholes model is a very useful tool on pricing options. First, an adaptive wavelet interpolation operator is constructed which can transform the nonlinear partial differential equations into a matrix of ordinary differential equations. Next, the VIM is developed to solve the nonlinear matrix differential equation, which is a new asymptotic analytical method for the nonlinear differential equations. Third, an adaptive precise integration method (PIM) for the system of ordinary differential equations is constructed, with which the almost exact numerical solution can be obtained. At last, the famous Black-Scholes model is taken as an example to test this new method. The numerical result shows the method’s higher numerical stability and precision.

### MSC:

 65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems 35G20 Nonlinear higher-order PDEs 65T60 Numerical methods for wavelets 91G60 Numerical methods (including Monte Carlo methods) 91B24 Microeconomic theory (price theory and economic markets)
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