Class Of Third Order Research Articles

Quintic B-Spline Technique for Numerical Treatment of Third Order Singular Perturbed Delay Differential Equation

In this paper, a class of third order singularly perturbed delay differential equation with large delay is considered for numerical treatment. The considered equation has discontinuous convection-diffusion coefficient and source term. A quintic trigonometric B-spline collocation technique is used for numerical simulation of the considered singularly perturbed delay differential equation by dividing the domain into the uniform mesh. Further, uniform convergence of the solution is discussed by using the concept of Hall error estimation and the method is found to be of first-order convergent. The existence of the solution is also established. Computation work is carried out to validate the theoretical results.

Fitted Finite Difference Method for Third Order Singularly Perturbed Delay Differential Equations of Convection Diffusion Type

In this paper, a fitted finite difference method on Shishkin mesh is suggested to solve a class of third order singularly perturbed boundary value problems for ordinary delay differential equations of convection-diffusion type. Numerical solution converges uniformly to the exact solution. The order of convergence of the numerical method is almost first order. Numerical results are provided to illustrate the theoretical results.

Finite difference scheme for third order singularly perturbed delay differential equation of convection diffusion type with integral boundary condition

A class of third order singularly perturbed delay differential equations of convection diffusion type with integral boundary condition is considered. A numerical method based on a finite difference scheme on a Shishkin mesh is presented. The method suggested is almost first order convergent. An error estimate is derived in the discrete norm. Numerical examples are presented, which validate the theoretical estimates.

Fitted finite difference method for third order singularly perturbed convection diffusion equations with integral boundary condition

A class of third order singularly perturbed convection diffusion type equations with integral boundary condition is considered. A numerical method based on a finite difference scheme on a Shishkin mesh is presented. The method suggested is of almost first order convergent. An error estimate is derived in the discrete norm. Numerical examples are presented, which validate the theoretical estimates.

An ε-uniform numerical method for third order singularly perturbed delay differential equations with discontinuous convection coefficient and source term

A class of third order singularly perturbed Boundary Value Problems (BVPs) for ordinary delay differential equations with discontinuous convection–diffusion coefficient and source term is considered in this paper. The existence and uniqueness of the solution has been proved. Further, a fitted finite difference method on Shishkin mesh is suggested to solve the problem. Numerical solution converges uniformly to the exact solution. The order of convergence of the numerical method presented here is of almost first order. Numerical results are provided to illustrate the theoretical results.

On the Oscillations of Nonlinear Third Order Neutral Differential Equations

This paper is concerned with the oscillation of solutions of a class of third order nonlinear neutral differential equations. New sufficient conditions guarantee that every solution is either oscillatory or tends to zero are given. The obtained results improve some recent published results in the literature. Some illustrative examples are given.

A rational spectral collocation method for third-order singularly perturbed problems

A new numerical method is developed for solving a class of third-order singularly perturbed boundary value problems. First of all, the given problem is transformed into a system of two ordinary dif...

Fixed point theorems for alpha-contractive mappings of Meir–Keeler type and applications

In this paper, we introduce the notion of α-contractive mapping of Meir–Keeler type in complete metric spaces and prove new theorems which assure the existence, uniqueness and iterative approximation of the fixed point for this type of contraction. The presented theorems extend, generalize and improve several existing results in literature. To validate our results, we establish the existence and uniqueness of solution to a class of third order two point boundary value problems.

Asymptotic - Numerical Method for Third-Order Singular Perturbation Problems

ABSTRACT In this paper, a class of third order singularly perturbed boundary value problems with suitable boundary conditions is considered. The third order boundary value problem is transformed to asymptotically equivalent second order boundary value problem. This problem is solved efficiently by using fitted Numerov method. Linear and non-linear examples are solved to illustrate the method and relative errors with L2-norms are presented to support the method.