Exponentially fitted block backward differentiation formulas for pricing options

To analyze the transient response of transformer windings under very fast transient over-voltage (VFTO), multi-conductor transmission line (MTL) model based on the representation of transformer windings by its individual turns are established. Space discretization is needed for solving the time-domain telegraph equations of MTL. To calculate the voltage distributions along transformer windings, through combining the compact finite difference (CFD) theory and the backward differentiation formulas (BDF). Simulation software ATP is introduced, and the simulation results demonstrate that the proposed approach is feasible.

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Parameter range reduction for ODE models using cumulative backward differentiation formulas

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2006.03.018 ◽

2007 ◽

Vol 203 (1) ◽

pp. 87-102 ◽

Cited By ~ 10

Author(s):

Allan R. Willms

Keyword(s):

Parameter Range ◽

Range Reduction ◽

Ode Models ◽

Backward Differentiation Formulas ◽

Differentiation Formulas

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Numerical Techniques for Unsteady Nonlinear Burgers Equation Based on Backward Differentiation Formulas

Nonlinear Engineering ◽

10.1515/nleng-2017-0068 ◽

2018 ◽

Vol 7 (3) ◽

pp. 171-181 ◽

Cited By ~ 1

Author(s):

Vijitha Mukundan ◽

Ashish Awasthi

Keyword(s):

Numerical Solutions ◽

Burgers Equation ◽

Numerical Technique ◽

System Stability ◽

Test Problems ◽

Numerical Techniques ◽

Ode System ◽

Backward Differentiation Formulas ◽

Nonlinear Ode ◽

Differentiation Formulas

AbstractWe introduce new numerical techniques for solving nonlinear unsteady Burgers equation. The numerical technique involves discretization of all variables except the time variable which converts nonlinear PDE into nonlinear ODE system. Stability of the nonlinear system is verified using Lyapunov’s stability criteria. Implicit stiff solvers backward differentiation formula of order one, two and three are used to solve the nonlinear ODE system. Four test problems are included to show the applicability of introduced numerical techniques. Numerical solutions so obtained are compared with solutions of existing schemes in literature. The proposed numerical schemes are found to be simple, accurate, fast, practical and superior to some existing methods.

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Block Backward Differentiation Formulas for Fractional Differential Equations

International Journal of Engineering Mathematics ◽

10.1155/2015/650425 ◽

2015 ◽

Vol 2015 ◽

pp. 1-14 ◽

Cited By ~ 3

Author(s):

T. A. Biala ◽

S. N. Jator

Keyword(s):

Numerical Approximation ◽

Initial Value ◽

One Dimensional ◽

Numerical Tests ◽

Numerical Integrators ◽

Backward Differentiation Formulas ◽

Collocation Approach ◽

Fractional Differential ◽

Large Systems ◽

Differentiation Formulas

This paper concerns the numerical approximation of Fractional Initial Value Problems (FIVPs). This is achieved by constructing k-step continuous BDFs. These continuous schemes are developed via the interpolation and collocation approach and are used to obtain the discrete k-step BDF and (k-1) additional methods which are applied as numerical integrators in a block-by-block mode for the integration of FIVP. The properties of the methods are established and regions of absolute stability of the methods are plotted in the complex plane. Numerical tests including large systems arising form the semidiscretization of one-dimensional fractional Burger’s equation show that the methods are highly accurate and efficient.

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