Related papers: An Extended Cubic B-spline Finite Element Method f…
In the present study, we solve initial boundary value problem construted on nonlinear Klein-Gordon equation. The collocation method on exponential cubic B-spline functions forming a set of basis for the functions defined in the same…
This paper proposes a strategy to solve the problems of the conventional s-version of finite element method (SFEM) fundamentally. Because SFEM can reasonably model an analytical domain by superimposing meshes with different spatial…
Spectral methods are renowned for their high accuracy and efficiency in solving partial differential equations. The Fourier pseudo-spectral method is limited to periodic domains and suffers from Gibbs oscillations in non-periodic problems.…
A generalization of classical cubic B-spline functions with a parameter is used as basis in the collocation method. Some initial boundary value problems constructed on the nonlinear Klein-gordon equation are solved by the proposed method…
Traditional finite element approaches are well-known to introduce spurious oscillations when applied to advection-dominated problems. We explore alleviation of this issue from the perspective of a generalized finite element formulation,…
Spline functions have long been used in numerically solving differential equations. Recently it revives as isogeometric analysis, which uses NURBS for both parametrization and element functions. In this paper, we introduce some multivariate…
In this article, we propose a fully-discrete scheme for the numerical solution of a nonlinear time-fractional biharmonic problem. This problem is first converted into an equivalent system by introducing a new variable. Then spatial and…
In this paper, we propose a numerical method for approximating the solution of a Cauchy singular integral equation defined on a closed, smooth contour in the complex plane. The coefficients and the right-hand side of the equation are…
In this paper we present a method for knot insertion and degree elevation of generalized B-splines (GB-splines) via the local representation of these curves as piecewise functions. The use of local structures makes the refinement routines…
The analysis of a delayed generalized Burgers-Huxley equation (a non-linear advection-diffusion-reaction problem) with weakly singular kernels is carried out in this work. Moreover, numerical approximations are performed using the…
In this work we address the analysis of the stationary generalized Burgers-Huxley equation (a nonlinear elliptic problem with anomalous advection) and propose conforming, nonconforming and discontinuous Galerkin finite element methods for…
In this paper we present a method for direct evaluation of generalized B-splines (GB-splines) via the local representation of these curves as piecewise functions. To accomplish this we introduce a local structure that makes GB-spline curves…
We derive a-priori error estimates for the finite-element approximation of a distributed optimal control problem governed by the steady one-dimensional Burgers equation with pointwise box constraints on the control. Here the approximation…
In this paper, we present an iterative reproducing kernel method for numerical solution of one dimensional fractional Burgers equation with variable coefficient. Convergence analysis is constructed theoretically. Numerical experiments show…
In this paper, B-spline collocation method is developed for the solution of one-dimensional hyperbolic telegraph equation. The convergence of the method is proved. Also the method is applied on some test examples, and the numerical results…
This work presents a collocation method for solving linear Fredholm integral equations of the second kind defined on a closed contour in the complex plane. The right-hand side of the equation is a piecewise continuous function that may have…
We develop a numerical method for solving the boundary value problem of The Linear Seventh Ordinary Boundary Value Problem by using seventh degree B-Spline function. Formulation is based on particular terms of order of seventh order…
In this paper, the numerical approximation of the generalized Burgers'-Huxley equation (GBHE) with weakly singular kernels using non-conforming methods will be presented. Specifically, we discuss two new formulations. The first formulation…
The well-known analytical solution of Burgers' equation is extended to curvilinear coordinate systems in three-dimensions by a method which is much simpler and more suitable to practical applications than that previously used. The results…
We consider an initial value problem for a quadratically nonlinear inviscid Burgers-Hilbert equation that models the motion of vorticity discontinuities. We use a normal form transformation, which is implemented by means of a near-identity…