Rafael Company¹, Vera N. Egorova², Lucas Jódar^1,*, Ferran Fuster Valls³

CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.2, pp. 493-508, 2020, DOI:10.32604/cmes.2020.010208 - 20 July 2020

Abstract A numerical method for American options pricing on assets under the Heston stochastic volatility model is developed. A preliminary transformation is applied to remove the mixed derivative term avoiding known numerical drawbacks and reducing computational costs. Free boundary is treated by the penalty method. Transformed nonlinear partial differential equation is solved numerically by using the method of lines. For full discretization the exponential time differencing method is used. Numerical analysis establishes the stability and positivity of the proposed method. The numerical convergence behaviour and effectiveness are investigated in extensive numerical experiments. More >

C.-W. Chang¹, C.-S. Liu², J.-R. Chang^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.1, pp. 13-38, 2005, DOI:10.3970/cmes.2005.010.013

Abstract In this paper, the inverse heat conduction problem governed by sideways heat equation is investigated numerically. The problem is ill-posed because the solution, if it exists, does not depend continuously on the data. To begin with, this ill-posed problem is analyzed by considering the stability of the semi-discretization numerical schemes. Then the resulting ordinary differential equations at the discretized times are numerically integrated towards the spatial direction by the group preserving scheme, and the stable range of the index r = 1/2ν Δt is investigated. When the numerical results are compared with exact solutions, it More >