‎second derivative general linear methods (sglms) as an extension‎ ‎of general linear methods (glms) have been introduced to improve‎ ‎the stability and accuracy properties of glms‎. ‎the coefficients of‎ ‎sglms are given by six matrices‎, ‎instead of four matrices for‎ ‎glms‎, ‎which are obtained by solving nonlinear systems of order and‎ ‎usually runge--kutta stability conditions‎. ‎in this p...

Numerical methods are needed for derivatives pricing in cases where analytic solutions are either unavailable or not easily computable. Examples of the former case include American-style options and most discretely observed path-dependent options. Examples of the latter type include the analytic formula for valuing continuously observed Asian options in [28], which is very hard to calculate for...

‎Second derivative general linear methods (SGLMs) as an extension‎ ‎of general linear methods (GLMs) have been introduced to improve‎ ‎the stability and accuracy properties of GLMs‎. ‎The coefficients of‎ ‎SGLMs are given by six matrices‎, ‎instead of four matrices for‎ ‎GLMs‎, ‎which are obtained by solving nonlinear systems of order and‎ ‎usually Runge--Kutta stability conditions‎. ‎In this p...

Predictor-corrector (PC) methods for the numerical solution of stiff ODEs can be extended to include the second derivative of the solution. In this paper, we consider second derivative PC methods with the three-step second derivative Adams-Bashforth as predictor and two-step second derivative Adams-Moulton as corrector which both methods have order six. Implementation of the proposed PC method ...

the aim of this paper is to present a new numerical method for solving the bagley-torvik equation. this equation has an important role in fractional calculus. the fractional derivatives are described based on the caputo sense. some properties of the sinc functions required for our subsequentdevelopment are given and are utilized to reduce the computation of solution of the bagley-torvik equatio...

in this paper, we apply the local fractional adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of fredholm integral equations of the second kind within local fractional derivative operators. the iteration procedure is based on local fractional derivative. the obtained results reveal that the proposed methods are very efficient and simple tools ...