Topic
Finite difference
About: Finite difference is a research topic. Over the lifetime, 19693 publications have been published within this topic receiving 408603 citations.
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TL;DR: The approach can be used to value any derivative security dependent on a single state variable and can be extended to deal with many derivative security pricing problems where there are several state variables.
Abstract: This paper suggests a modification to the explicit finite difference method for valuing derivative securities. The modification ensures that, as smaller time intervals are considered, the calculated values of the derivative security converge to the solution of the underlying differential equation. It can be used to value any derivative security dependent on a single state variable and can be extended to deal with many derivative security pricing problems where there are several state variables. The paper illustrates the approach by using it to value bonds and bond options under two different interest rate processes.
377 citations
TL;DR: In this article, a shallow water wave equation is developed from the primitive two-dimensional shallow water equation, and a finite element model based on this equation and the primitive momentum equation are developed.
374 citations
TL;DR: In this article, the Laplace transform for the nabla derivative on the time scale of integers is introduced and properties of discrete fractional calculus in the sense of a backward difference are introduced and developed.
Abstract: Properties of discrete fractional calculus in the sense of a backward difference are introduced and developed. Exponential laws and a product rule are developed and relations to the forward fractional calculus are explored. Properties of the Laplace transform for the nabla derivative on the time scale of integers are developed and a fractional finite difference equation is solved with a transform method. As a corollary, two new identities for the gamma function are exhibited.
372 citations
TL;DR: In this paper, a simulation model of finite differences describing a double-glass multi-crystalline photovoltaic module has been developed and validated using experimental data from such a PV module.
372 citations
TL;DR: In this paper, the frequency-dependent characteristics of the microstrip discontinuities have been analyzed using full-wave approaches and the time-domain finite-difference (TD-FD) method is presented.
Abstract: The frequency-dependent characteristics of the microstrip discontinuities have previously been analyzed using full-wave approaches. The time-domain finite-difference (TD-FD) method presented here is an independent approach and is relatively new in its application for obtaining the frequency-domain results for microwave components. The validity of the TD-FD method in modeling circuit components for MMIC CAD applications is established. >
372 citations