Sinc-collocation Method Research Articles

Sinc-collocation method for solving sodium alginate (SA) non-Newtonian nanofluid flow between two vertical flat plates

This paper seeks to develop an efficient method for solving natural convection of a non-Newtonian nanofluid flow between two vertical flat plates. Sodium alginate is considered as the non-Newtonian fluid, and then two distinct types of nanoparticles, namely silver and copper, are added to it. To do so, the governing boundary layer and temperature equations are reduced to a set of ordinary differential equations. This approach is based on a global collocation method using Sinc basis functions, and the resulting set of ordinary differential equations are replaced by a system of algebraic equations. It is well known that the Sinc procedure converges to the solution at an exponential rate. Numerical results are included to demonstrate the validity and applicability of the method, and a comparison is made with the existing results. Also, the effect of various parameters such as Prandtl number (Pr), dimensionless non-Newtonian viscosity number $$(\delta )$$ and nanoparticle volume fraction ( $$\phi $$ ) on non-dimensional velocity and temperature profiles are discussed. It was concluded from this study that velocity and temperature increased with increasing Pr. Moreover, our results indicate that both the velocity and temperature decrease as $$\delta $$ increases. Finally, the results demonstrated that, when $$\phi $$ increases, the velocity increases but the temperature values decrease.

APPROXIMATE SOLUTIONS OF FRACTIONAL BOUNDARY VALUE PROBLEMS BASED ON BETA FRACTIONAL DERIVATIVE

In this work, we consider some fractional differential equations with different boundary conditions. Sinc-collocation method (SCM) has been employed to obtain the approximate solution for these fractional boundary value problems (FBVPs). Beta-derivative is taken for the fractional derivatives. Intercalarity, several test samples with numerical simulations are handled. Convergence analysis shows that SCM is a consistent and effective method.

A collocation method for solving boundary value problems of fractional order

In this paper, the sinc collocation method is used to obtain the solution of the second-order fractional boundary value problems based on the conformable fractional derivative. For this purpose a theorem is proved to represent the terms having fractional derivatives in terms of sinc basis functions. To show the efficiency and accuracy of the present method, some problems are solved and the obtained solutions are compared with the approximate solutions obtained by using the other numerical methods as well as the exact solutions of the problems.

A numerical algorithm for the solution of nonlinear fractional differential equations via beta‐derivatives

In this paper, the sinc‐collocation method (SCM) is investigated to obtain the solution of the nonlinear fractional order differential equations based on the relatively new defined fractional derivative, beta‐derivative. For this purpose, a theorem is proved for the approximate solution obtained from the SCM. Moreover, convergence analysis of the SCM is presented. To show the efficiency and the simplicity of the proposed method, some examples are solved, and the results are compared with the exact solutions of the considered equations.

The Impact of Two Transformations on the Solutions of Second Kind Fredholm Integral Equations System

The Sinc-collocation method using the single and double exponential transformations has been established to solve the second kind FIEs linear systems. The convergence analyses of the approach have been discussed and the exponential convergence rates have been obtained for both of the transformations. The method has been tested by examples and compared with various well-known methods, including the homotopy perturbation method, modified homotopy perturbation method, triangular functions method, adaptive method, B-spline wavelet collocation method, block-pulse functions, orthogonal triangular functions, and rationalized Haar functions method. It justifies that the presented method converges exponentially, bears the outstanding accuracy with less errors and computational effort compared to the discussed methods.

The Solution of Fuzzy Integral Equation by Using Sinc Collocation Method

The Solution of Fuzzy Integral Equation by Using Sinc Collocation Method

A solution method for integro-differential equations of conformable fractional derivative

The aim of this work is to determine an approximate solution of a fractional order Volterra-Fredholm integro-differential equation using by the Sinc-collocation method. Conformable derivative is considered for the fractional derivatives. Some numerical examples having exact solutions are approximately solved. The comparisons of the exact and the approximate solutions of the examples are presented both in tables and graphical forms.

Numerical solution of Volterra partial integro-differential equations based on sinc-collocation method

We provide the numerical solution of a Volterra integro-differential equation of parabolic type with memory term subject to initial boundary value conditions. Finite difference method in combination with product trapezoidal integration rule is used to discretize the equation in time and sinc-collocation method is employed in space. A weakly singular kernel has been viewed as an important case in this study. The convergence analysis has been discussed in detail, which shows that the approach exponentially converges to the solution. Furthermore, numerical examples and illustrations are presented to prove the validity of the suggested method.

Double exponential sinc-collocation method for solving the energy eigenvalues of harmonic oscillators perturbed by a rational function

We show that the double exponential sinc-collocation method provides an efficient uniformly accurate solution to the one-dimensional time independent Schrödinger equation for a general class of rational potentials of the form V (x) = p(x)/q(x). The derived algorithm is based on the discretization of the Hamiltonian of the Schrödinger equation using sinc expansions. This discretization results in a generalized eigenvalue problem, the eigenvalues of which correspond to approximations of the energy values of the starting Hamiltonian. A systematic numerical study is conducted, beginning with test potentials with known eigenvalues and moving to rational potentials of increasing degree.

Eventual periodicity of the forced oscillations for a Korteweg–de Vries type equation on a bounded domain using a sinc collocation method

We demonstrate numerically the eventual time periodicity of solutions u ( . , t ) to the Korteweg–de Vries type equation with periodic forcing at one end using the sinc-collocation method. This method approximates the space dimension of the solution with a cardinal expansion of sinc functions, thus allowing the avoidance of a costly finite difference grid for a third order boundary value problem. The first order time derivative is approximated with a θ -weighted finite difference method. The sinc-collocation method was found to be more robust and more efficient than other numerical schemes when applied to this problem.

On the Computation of Eigenvalues of the Anharmonic Coulombic Potential

In this work, we propose a method combining the Sinc collocation method with the double exponential transformation for computing the eigenvalues of the anharmonic Coulombic potential. We introduce a scaling factor that improves the convergence speed and the stability of the method. Further, we apply this method to Coulombic potentials leading to a highly efficient and accurate computation of the eigenvalues.

An efficient scheme for solving a system of fractional differential equations with boundary conditions

In this study, the sinc collocation method is used to find an approximate solution of a system of differential equations of fractional order described in the Caputo sense. Some theorems are presented to prove the applicability of the proposed method to the system of fractional order differential equations. Some numerical examples are given to test the performance of the method. Approximate solutions are compared with exact solutions by examples. Some graphs and tables are presented to show the performance of the proposed method.

Theoretical analysis of Sinc-collocation methods and Sinc-Nyström methods for systems of initial value problems

A Sinc-collocation method has been proposed by Stenger, and he also gave theoretical analysis of the method in the case of a `scalar' equation. This paper extends the theoretical results to the case of a `system' of equations. Furthermore, this paper proposes more efficient method by replacing the variable transformation employed in Stenger's method. The efficiency is confirmed by both of theoretical analysis and numerical experiments. In addition to the existing and newly-proposed Sinc-collocation methods, this paper also gives similar theoretical results for Sinc-Nystr\"{o}m methods proposed by Nurmuhammad et al. From a viewpoint of the computational cost, it turns out that the newly-proposed Sinc-collocation method is the most efficient among those methods.

Approximate solutions of Volterra-Fredholm integro-differential equations of fractional order

In this study, sinc-collocation method is introduced for solving Volterra-Fredholm integrodifferential equations of fractional order. Fractional derivative is described in the Caputo sense. Obtained results are given to literature as a new theorem. Some numerical examples are presented to demonstrate the theoretical results.

Approximate Solution Of Singular Integral Equation By Sinc Function

In this paper we present a method for numerical solution of singular integral equation with Cauchy kernel of first kind using sinc-collocation method. Sinc functions are used to drive an approximate solution. Moreover, an absolute error is computed for the numerical solution

A numerical method for solution of integro-differential equations of fractional order

Bu calismada, sinc siralama yontemi kesirli mertebeden Volterra integro-diferansiyel denklemleri yaklasik olarak cozmek icin gelistirilmistir. Kesirli turev, kesirli analizde sikca kullanilan Caputo anlaminda tanimlanmistir. Elde edilen sonuclar iki yeni teorem ile verilmistir. Bazi sayisal ornekleri teorik sonuclari gostermek icin sunulmustur.

Sinc Collocation Solutions for the Integral Algebraic Equation of Index-1

AbstractIn this article, Sinc collocation method is considered to obtain the numerical solution of integral algebraic equation of index-1 by reducing it to an explicit system of algebraic equation. It is shown that Sinc collocation solution can produce an error of order. Moreover, Sinc method is applied to several examples to illustrate the accuracy and implementation of the method.

The double exponential sinc collocation method for singular Sturm-Liouville problems

Sturm-Liouville problems are abundant in the numerical treatment of scientific and engineering problems. In the present contribution, we present an efficient and highly accurate method for computing eigenvalues of singular Sturm-Liouville boundary value problems. The proposed method uses the double exponential formula coupled with sinc collocation method. This method produces a symmetric positive-definite generalized eigenvalue system and has exponential convergence rate. Numerical examples are presented and comparisons with single exponential sinc collocation method clearly illustrate the advantage of using the double exponential formula.

Sinc numerical solution for pantograph Volterra delay-integro-differential equation

ABSTRACTIn this article, Sinc collocation method is considered to obtain the numerical solution of pantograph Volterra delay-integro-differential equation (VDIDE). This numerical method reduces the VDIDE to an explicit system of algebraic equation. Convergence analysis is given and shows that Sinc solution produces an error of order , where k>0 is a constant. Moreover, Sinc method is applied to the test examples to illustrate accuracy and implementation of the method.

Using Sinc-collocation method for solving weakly singular Fredholm integral equations of the first kind

In this paper, Sinc-collocation method is used to approximate the solution of weakly singular nonlinear Fredholm integral equations of the first kind. Some of the important advantages of this method are rate of convergence of an approximate solution and simplicity for performing even in the presence of singularities. The convergence analysis of the proposed method is proved by preparing the theorems which show the errors decay exponentially and guarantee the applicability of that. Finally, several numerical examples are considered to show the capabilities, validity, and accuracy of the numerical scheme.