**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32718

##### A Review on Higher Order Spline Techniques for Solving Burgers Equation Using B-Spline Methods and Variation of B-Spline Techniques

**Authors:**
Maryam Khazaei Pool,
Lori Lewis

**Abstract:**

This is a summary of articles based on higher order B-splines methods and the variation of B-spline methods such as Quadratic B-spline Finite Elements Method, Exponential Cubic B-Spline Method Septic B-spline Technique, Quintic B-spline Galerkin Method, and B-spline Galerkin Method based on the Quadratic B-spline Galerkin method (QBGM) and Cubic B-spline Galerkin method (CBGM). In this paper we study the B-spline methods and variations of B-spline techniques to find a numerical solution to the Burgers’ equation. A set of fundamental definitions including Burgers equation, spline functions, and B-spline functions are provided. For each method, the main technique is discussed as well as the discretization and stability analysis. A summary of the numerical results is provided and the efficiency of each method presented is discussed. A general conclusion is provided where we look at a comparison between the computational results of all the presented schemes. We describe the effectiveness and advantages of these methods.

**Keywords:**
Burgers’ Equation,
Septic B-spline,
Modified Cubic
B-Spline Differential Quadrature Method,
Exponential Cubic
B-Spline Technique,
B-Spline Galerkin Method,
and Quintic B-Spline
Galerkin Method.

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