This paper adapts the hybrid method, a combination of the Laplace transformation and the finite-difference approach, to the pricing of barrier-style options. The hybrid method eliminates the time steps and provides a highly accurate and precise numerical solution that can be rapidly obtained....

Slope failure is very common phenomenon in hilly regions, especially in young techno active mountainous like Himalayas. It is hazardous because of the accompanying progressive movement of the slope-forming material. In order to minimize the landslide effects, slope failure analysis and...

In this work we improve the algorithm of Han and Wu [SIAM J. Numer. Anal. 41 (2003), 2081–2095] for American Options with respect to stability, accuracy and order of computational effort. We derive an exact discrete artificial boundary condition (ABC) for the Crank–Nicolson scheme for...

The coupled nonlinear Schrödinger equation models several intersting physical phenomena. It presents a model equation for optical fiber with linear birefringence. In this paper, we present a linearly implicit conservative method to solve this equation. This method is second order accurate in...

A rational approximant of third order, which is applied to a three-time level recurrence relation, is used to transform the two-dimensional sine-Gordon (SG) equation into a second-order initial-value problem. The resulting nonlinear finite-difference scheme, which is analyzed for stability, is...

This paper presents a 3D model for pricing defaultable bonds with embedded put/call options. The pricing model incorporates three essential ingredients in the pricing of defaultable bonds: stochastic interest rate, stochastic default risk, and put/call provision. Both the stochastic interest...

In this paper, we consider the solution of the modified Burger's equation by using the collocation method with quintic splines. Applying the Von-Neumann stability analysis method we show that the proposed method is unconditionally stable. By conducting a comparison between the absolute error for...