Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation

Convergence of a high-order compact finite difference scheme for a nonlinear Black--Scholes equation

A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the disc...

Convergence of an Eighth-Order Compact Difference Scheme for the Nonlinear Schrödinger Equation

A new compact difference scheme is proposed for solving the nonlinear Schrödinger equation. The scheme is proved to conserve the total mass and the total energy and the optimal convergent rate, without any restriction on the grid ratio, at the order of O h8 τ2 in the discrete L∞-norm with time step τ and mesh size h. In numerical analysis, beside the standard techniques of the energy method, a ...

High order compact finite difference schemes for a nonlinear Black-Scholes equation

High Order Compact Finite Difference Schemes for Solving Bratu-Type Equations

In the present study, high order compact finite difference methods is used to solve one-dimensional Bratu-type equations numerically. The convergence analysis of the methods is discussed and it is shown that the theoretical order of the method is consistent with its numerical rate of convergence. The maximum absolute errors in the solution at grid points are calculated and it is shown that the ...

A Compact Fourth-order Finite Difference Scheme for the Improved Boussinesq Equation with Damping Terms

Fuqiang Lu, Zhiyao Song and Zhuo Zhang Key Laboratory of Virtual Geographic Environment (Nanjing Normal University), Ministry of Education, Nanjing, 210023, China State Key Laboratory Cultivation Base of Geographical Environment Evolution (Jiangsu Province), Nanjing, 210023, China Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanji...