Based on the Legendre pseudospectral method, we propose a numerical treatment for pricing perpetual American put option with stochastic volatility. In this simple approach, a nonlinear algebraic equation system is first derived, and then solved by the Gauss-Newton algorithm. The convergence of the current scheme is ensured by constructing a test example similar to the original problem, and comp...

Preserving in the discrete realm the underlying geometric, topological, and algebraic structures at stake in partial differential equations has proven to be a fruitful guiding principle for numerical methods in a variety of fields such as elasticity, electromagnetism, or fluid mechanics. However, structure-preserving methods have traditionally used spaces of piecewise polynomial basis functions...

Gibbs phenomenon is the particular manner how a global spectral approximation of a piecewise analytic function behaves at the jump discontinuity. The truncated spectral series has large oscillations near the jump, and the overshoot does not decay as the number of terms in the truncated series increases. There is therefore no convergence in the maximum norm, and convergence in smooth regions awa...

This paper is devoted to implementing the Legendre spectral collocation method to introduce numerical solutions of a certain class of fractional variational problems (FVPs). The properties of the Legendre polynomials and Rayleigh-Ritz method are used to reduce the FVPs to the solution of system of algebraic equations. Also, we study the convergence analysis. The obtained numerical results show ...

An analytic technique involving a transftirmation on the Chebychev transfer function is presented in this paper. This method will enable the designer to reduce the value of the spike in the group-delay projile at the expense of the stopband roll-ofS rate, while maintaining a pre-spec$ed equi-ripple characteristic in the passband. Since the parameters of the transformation are continuous-valued,...

In solving semilinear initial boundary value problems with prescribed non-periodic boundary conditions using implicit-explicit and implicit time stepping schemes, both the function and derivatives of the function may need to be computed accurately at each time step. To determine the best Chebyshev collocation method to do this, the accuracy of the real space Chebyshev differentiation, spectral ...