Nonstandard Finite Difference Schemes with Application to Finance: Option Pricing

2000 Mathematics Subject Classification: 65M06, 65M12.

Low Volatility Options and Numerical Diffusion of Finite Difference Schemes

2000 Mathematics Subject Classification: 65M06, 65M12.

A Note on the “Constructing” of Nonstationary Methods for Solving Nonlinear Equations with Raised Speed of Convergence

This paper is partially supported by project ISM-4 of Department for Scientific Research, “Paisii Hilendarski” University of Plovdiv.

Optimal Control of a Second Order Parabolic Heat Equation

In this paper, we are concerned with the optimal control boundary control of a second order parabolic heat equation. Using the results in [Evtushenko, 1997] and spatial central finite difference with diagonally implicit Runge-Kutta method (DIRK) is applied to solve the parabolic heat equation. The conjugate gradient method (CGM) is applied to solve the distributed control problem. Numerical results are reported.

A Gradient-Type Optimization Technique for the Optimal Control for Schrodinger Equations

In this paper, we are considered with the optimal control of a schrodinger equation. Based on the formulation for the variation of the cost functional, a gradient-type optimization technique utilizing the finite difference method is then developed to solve the constrained optimization problem. Finally, a numerical example is given and the results show that the method of solution is robust.

Application of an Acceleration Scheme

In this paper we propose an optimized algorithm, which is faster compared to previously described finite difference acceleration scheme, namely the Modified Super-Time-Stepping (Modified STS) scheme for age-structured population models with difusion.

Application of an Acceleration Scheme for an Age-Structured Diffusion Model

In this paper we propose an optimized algorithm, which is faster compared to previously described finite difference acceleration scheme, namely the Modified Super-Time-Stepping (Modified STS) scheme for age- structured population models with diffusion.

Second Order Optimality Conditions in Nonsmooth Unconstrained Optimization

AMS subject classification: 49J52, 90C30.