In this paper existence and uniqueness of twelfth degree spline is proved with application to quadrature. This formula is in the class of splines of degree 12 and continuity order [Formula: see text] that matches the derivatives up to order 6 at the knots of a uniform partition. Some mistakes in the literature are pointed out and corrected. Numerical examples are given to illustrate the applica...

Based on the generalized differential quadrature method, an analysis method of p-delta effect for continuous distribution system is proposed. Firstly, structural with mass and stiffness taken as research object. principle virtual work, axial transverse vibration equations considering are given. Secondly, partial discretized by using dynamic ordinary obtained to analyze system. Finally, example ...

dynamic analysis of two-dimensional elasticity problems using the isogeometric analysis method and its comparison with the finite element method is the subject of this research. for this purpose, formulation of the governing differential equation is obtained by using the b-spline basis functions. some numerical examples employing consistent and lumped mass matrices are presented in order to com...

A numerical scheme, based on the cubic B-spline wavelets for solving fractional integro-differential equations is presented. The fractional derivative of these wavelets are utilized to reduce the fractional integro-differential equation to system of algebraic equations. Numerical examples are provided to demonstrate the accuracy and efficiency and simplicity of the method.

In this paper, we construct a numerical ‎method‎ to ‎the ‎solution ‎of‎ the Black-Scholes partial differential equation modeling the European option pricing problem with regard to a single asset‎. ‎W‎e use an explicit spline-difference scheme which is based on using a finite difference approximation for the temporal derivative and a cubic B-spline collocation for spatial derivatives. ‎The deriv...

This article aims to propose an efficient Fibonacci wavelet-based collocation method for solving the nonlinear reaction-diffusion equation of Fisher-type. The underlying numerical scheme starts by formulating operational matrices integration corresponding wavelets. Besides, we study error analysis and convergence theorem proposed technique. Subsequently, a set algebraic equations are formed giv...