Stochastic differential equations (SDEs) and the Kolmogorov partial differential equations
(PDEs) associated to them have been widely used in models from engineering, finance, and …

This book is designed to be used by mathematicians, engineers, and computer scientists as
a graduate-level introduction to numerical analysis and its methods. Readers are expected …

Nonlinear Black–Scholes equations have been increasingly attracting interest over the last
two decades, since they provide more accurate values by taking into account more realistic …

In this paper, we develop and analyze a high order compact finite difference method (CFDM)
for solving a general class of two-point nonlinear singular boundary value problems with …

We propose the use of the meshfree radial basis point interpolation (RBPI) to solve the Black–
Scholes model for European and American options. The RBPI meshfree method offers …

We develop a novel fourth-order compact finite difference scheme to solve nonlinear
singular ordinary differential equations. Such problems occur in many fields of science and …

The main aim of this paper is to construct a new computational approach for the numerical
solution of generalized Black–Scholes equation. In this approach, the temporal variable is …

This paper presents a high order numerical method based on a uniform mesh to obtain a
highly accurate result for generalized Black–Scholes equation arising in the financial …

This paper develops an efficient combined interpolation/finite element approach for solving
a three‐dimensional Black‐Scholes problem with stochastic volatility. The technique …

The homotopy perturbation method is designed to obtain a quick and accurate solution to
the Black–Scholes equation and boundary conditions for a European option pricing …