a new finite difference/spectral method for numerical solution of the black–scholes equation for european put options

The main purpose of this paper is to investigate a new numerical methodbased on backward finite difference method and spectral galerkin method for solvingblack–scholes equation for european put option. in this paper, by discretization intime for the black-scholes equation we get the ordinary system of differential equations(odes) in the spatial domain. the obtained odes is solved by applying the spectralgalerkin method based on the generalized jacobi polynomials. the convergence of themethod in suitable spaces of functions, equipped with the weighted l2- norm is discussed.also, we provide numerical experiment to show the accuracy of method.