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 ...

In this work, two multi-step derivative-free iterative methods are presented for solving system of nonlinear equations. The new methods have high computational efficiency and low computational cost. The order of convergence of the new methods is proved by a development of an inverse first-order divided difference operator. The computational efficiency is compared with the existing methods. Nume...

In this article, we have investigated solutions to a symmetry chaotic system with fractional derivative order using two different methods—the numerical scheme for the ABC derivative, and Laplace decomposition method, help from MATLAB Mathematica platforms. We explored progressive efficient model through successful implementation of mathematical methods. For phase portrait model, profiles chaos ...

Orthogonal decompositions (OD:s) that are monomial have been constructed for most simple Lie algebras but in some cases the existence of an OD is still an open question. One of them is Lie algebras of type Cn where n is not a power of 2. In this paper we use computational methods to prove that C3 has no monomial OD. 1 Orthogonal decompositions of simple Lie algebras The basic question, of which...

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...