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View article: Modeling of solitary waves via higher-order predictor-corrector scheme
Modeling of solitary waves via higher-order predictor-corrector scheme Open
The combination of the sextic b-spline collocation method and the predictor-corrector method is employed to discretize the Regularized Long Wave Equation (RLWE) fully into two systems of linear algebraic equations. Solution of the predicto…
View article: NUMERICAL SOLUTIONS OF REACTION-DIFFUSION EQUATION SYSTEMS WITH TRIGONOMETRIC QUINTIC B-SPLINE COLLOCATION ALGORITHM
NUMERICAL SOLUTIONS OF REACTION-DIFFUSION EQUATION SYSTEMS WITH TRIGONOMETRIC QUINTIC B-SPLINE COLLOCATION ALGORITHM Open
In this study, trigonometric quintic B-spline collocation method is constructed for computing numerical solutions of the reaction-diffusion system (RDS). Schnakenberg, Gray-Scott and Brusselator models are special cases of reaction-diffusi…
View article: CLASSIFICATION OF ANEMIA DISEASE USING ARTIFICIAL NEURAL NETWORKS METHODS
CLASSIFICATION OF ANEMIA DISEASE USING ARTIFICIAL NEURAL NETWORKS METHODS Open
Anemia, which occurs when the hemoglobin value falls below a certain reference range and is also called anemia, needs many blood tests, radiological images and analyzes for its diagnosis and treatment. In addition to such a large amount of…
View article: CUBIC B-SPLINE LEAST SQUARES METHOD FOR THE NUMERICAL SOLUTION OF ADVECTION-DIFFUSION EQUATION
CUBIC B-SPLINE LEAST SQUARES METHOD FOR THE NUMERICAL SOLUTION OF ADVECTION-DIFFUSION EQUATION Open
The least squares algorithm is set up for getting the solution of the time-dependent one-dimensional advection-diffusion equation (ADE). The cubic B-spline least squares method is coupled with the Crank-Nicolson scheme to produce the numer…
View article: Hyperbolic-trigonometric tension B-spline Galerkin approach for the solution of Fisher equation
Hyperbolic-trigonometric tension B-spline Galerkin approach for the solution of Fisher equation Open
A Galerkin finite element method is constructed for computing solution of the Fisher equation. Hyperbolic-trigonometric tension (HTT) B-splines are used as weight and shape functions in the Galerkin approach. Fully discretization of the Fi…
View article: Numerical Solution of Singularly Perturbed Problems via both Galerkin and Subdomain Galerkin methods
Numerical Solution of Singularly Perturbed Problems via both Galerkin and Subdomain Galerkin methods Open
In this paper, numerical solutions of singularly perturbed boundary value problems are given by using variants of finite element method. Both Galerkin and subdomain Galerkin method based on quadratic B-spline functions are applied over the…
View article: A NUMERICAL SOLUTION OF THE ADVECTION-DIFFUSION EQUATION BY USING EXTENDED CUBIC B-SPLINE FUNCTIONS
A NUMERICAL SOLUTION OF THE ADVECTION-DIFFUSION EQUATION BY USING EXTENDED CUBIC B-SPLINE FUNCTIONS Open
In this paper, numerical solution of theadvection-diffusion equation is obtained by using extended cubic B-splinefunctions. For space discretization, the extended cubic B-spline Galerkinmethod is used to integrate the advection-diffusion e…
View article: Numerical Solutions of the Gardner Equation by Extended Form of the\n Cubic B-splines
Numerical Solutions of the Gardner Equation by Extended Form of the\n Cubic B-splines Open
The extended definition of the polynomial B-splines may give a chance to\nimprove the results obtained by the classical cubic polynomial B-splines.\nDetermination of the optimum value of the extension parameter can be achieved\nby scanning…
View article: Numerical Solutions of the Gardner Equation by Extended Form of the Cubic B-splines
Numerical Solutions of the Gardner Equation by Extended Form of the Cubic B-splines Open
The extended definition of the polynomial B-splines may give a chance to improve the results obtained by the classical cubic polynomial B-splines. Determination of the optimum value of the extension parameter can be achieved by scanning so…
View article: The Numerical Approach to the Fisher's Equation via Trigonometric Cubic B-spline Collocation Method
The Numerical Approach to the Fisher's Equation via Trigonometric Cubic B-spline Collocation Method Open
In this study, we set up a numerical technique to get approximate solutions of Fisher's equation which is integrated fully with help of combination of the trigonometric cubic B-spline functions in space and Crank-Nicolson in time. Numerica…
View article: Wave Propagation by Way of Exponential B-Spline Galerkin Method
Wave Propagation by Way of Exponential B-Spline Galerkin Method Open
In this paper, the exponential B-spline Galerkin \ method is set up for getting the numerical solution of the Burgers' equation. Two numerical examples\ related to shock wave propogation and travelling wave are studied to illustrate the ac…
View article: Numerical investigation of the solutions of Schrodinger equation with exponential cubic B-spline finite element method
Numerical investigation of the solutions of Schrodinger equation with exponential cubic B-spline finite element method Open
In this paper, we investigate the numerical solutions of the cubic nonlinear Schrodinger equation via the exponential B-spline collocation method. Crank-Nicolson formulas are used for time discretization of the target equation. A lineariza…
View article: The Numerical Approach to the Fisher's Equation via Trigonometric Cubic\n B-spline Collocation Method
The Numerical Approach to the Fisher's Equation via Trigonometric Cubic\n B-spline Collocation Method Open
In this study, we set up a numerical technique to get approximate solutions\nof Fisher's equation which is one of the most important model equation in\npopulation biology. We integrate the equation fully by using combination of the\ntrigon…
View article: The Numerical Approach to the Fisher's Equation via Trigonometric Cubic B-spline Collocation Method
The Numerical Approach to the Fisher's Equation via Trigonometric Cubic B-spline Collocation Method Open
In this study, we set up a numerical technique to get approximate solutions of Fisher's equation which is one of the most important model equation in population biology. We integrate the equation fully by using combination of the trigonome…
View article: The Exponential Cubic B-spline Algorithm for Burgers's Equation
The Exponential Cubic B-spline Algorithm for Burgers's Equation Open
The exponential cubic B-spline functions are used to set up the collocation method for finding solutions of the Burgers's equation. The effect of the exponential cubic B-splines in the collocation method is sought by studying four text pro…
View article: A Trigonometric Cubic B-spline Finite Element Method for Solving the Nonlinear Coupled Burger Equation
A Trigonometric Cubic B-spline Finite Element Method for Solving the Nonlinear Coupled Burger Equation Open
The coupled Burgers equation is solved by way of the trigonometric B-spline collocation method. The unknown of the coupled Burgers equation is integrated in time by aid of the Crank-Nicolson method. Resulting time-integrated coupled Burger…
View article: Galerkin Method for the numerical solution of the advection-diffusion\n equation by using exponential B-splines
Galerkin Method for the numerical solution of the advection-diffusion\n equation by using exponential B-splines Open
In this paper, the exponential B-spline functions are used for the numerical\nsolution of the advection-diffusion equation. Two numerical examples\\ related\nto pure advection in a finitely long channel and the distribution of an initial\n…
View article: Galerkin Method for the numerical solution of the advection-diffusion equation by using exponential B-splines
Galerkin Method for the numerical solution of the advection-diffusion equation by using exponential B-splines Open
In this paper, the exponential B-spline functions are used for the numerical solution of the advection-diffusion equation. Two numerical examples\ related to pure advection in a finitely long channel and the distribution of an initial Gaus…
View article: Galerkin method for the numerical solution of the Burgers' equation by using exponential B-splines
Galerkin method for the numerical solution of the Burgers' equation by using exponential B-splines Open
In this paper, the exponential B-spline Galerkin \ method is set up for getting the numerical solution of the Burgers' equation. Two numerical examples\ related to shock wave propogation and travelling wave are studied to illustrate the ac…
View article: Numerical solutions of the reaction diffusion system by usingexponential cubic B-spline collocation algorithms
Numerical solutions of the reaction diffusion system by usingexponential cubic B-spline collocation algorithms Open
The solutions of the reaction-diffusion system are given by method of collocation based on the exponential B-splines. Thus the reaction-diffusion systemturns into an iterative banded algebraic matrix equation. Solution of the matrix equati…
View article: Trigonometric quadratic B-spline subdomainGalerkin algorithm for the Burgers’ equation
Trigonometric quadratic B-spline subdomainGalerkin algorithm for the Burgers’ equation Open
A variant of the subdomain Galerkin method has been set up to find numerical solutions of the Burgers’ equation. Approximate function consists of the combination of the trigonometric B-splines. Integration of Burgers’ equation has been ach…
View article: Galerkin Method for the numerical solution of the RLW equation by using exponential B-splines
Galerkin Method for the numerical solution of the RLW equation by using exponential B-splines Open
In this paper, the exponential B-spline functions are used for the numerical solution of the RLW equation. Three numerical examples related to propagation of single solitary wave, interaction of two solitary waves and wave generation are e…
View article: The Exponential Cubic B-Spline Algorithm for Korteweg-de Vries Equation
The Exponential Cubic B-Spline Algorithm for Korteweg-de Vries Equation Open
The exponential cubic B-spline algorithm is presented to find the numerical solutions of the Korteweg-de Vries (KdV) equation. The problem is reduced to a system of algebraic equations, which is solved by using a variant of Thomas algorith…