Bernoulli Matrix Approach for Solving Two Dimensional Linear Hyperbolic Partial Differential Equations with Constant Coefficients

2012 ◽  
Vol 2 (4) ◽  
pp. 136-139 ◽  
Author(s):  
Emran Tohidi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Hyperbolic Partial Differential Equations ◽  
Two Dimensional ◽  
Matrix Approach ◽  
Partial Differential ◽  
Constant Coefficients

scholarly journals A matrix approach to solving hyperbolic partial differential equations using Bernoulli polynomials

Filomat ◽  
2016 ◽  
Vol 30 (4) ◽  
pp. 993-1000 ◽  
Author(s):  
Bicer Erdem ◽  
Salih Yalcinbas
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Error Analysis ◽  
Matrix Equation ◽  
Bernoulli Polynomials ◽  
Hyperbolic Partial Differential Equations ◽  
Matrix Approach ◽  
Residual Function ◽  
Partial Differential ◽  
The Matrix

The present study considers the solutions of hyperbolic partial differential equations. For this, an approximate method based on Bernoulli polynomials is developed. This method transforms the equation into the matrix equation and the unknown of this equation is a Bernoulli coefficients matrix. To demostrate the validity and applicability of the method, an error analysis developed based on residual function. Also examples are presented to illustrate the accuracy of the method.

Cosine expansion based differential quadrature algorithm for numerical simulation of two dimensional hyperbolic equations with variable coefficients

2015 ◽  
Vol 25 (7) ◽  
pp. 1574-1589 ◽  
Author(s):  
Anjali Verma ◽  
Ram Jiwari
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Hyperbolic Equations ◽  
Second Order ◽  
Differential Quadrature ◽  
Hyperbolic Partial Differential Equations ◽  
Two Dimensional ◽  
Nonlinear Hyperbolic Equations ◽  
Partial Differential ◽  
Content Type

Purpose – The purpose of this paper is to present the computational modeling of second-order two-dimensional nonlinear hyperbolic equations by using cosine expansion-based differential quadrature method (CDQM). Design/methodology/approach – The CDQM reduced the equations into a system of second-order differential equations. The obtained system is solved by RK4 method by converting into a system of first ordinary differential equations. Findings – The computed numerical results are compared with the results presented by other workers (Mohanty et al., 1996; Mohanty, 2004) and it is found that the present numerical technique gives better results than the others. Second, the proposed algorithm gives good accuracy by using very less grid point and less computation cost as comparison to other numerical methods such as finite difference methods, finite elements methods, etc. Originality/value – The author extends CDQM proposed in (Korkmaz and Dağ, 2009b) for two-dimensional nonlinear hyperbolic partial differential equations. This work is new for two-dimensional nonlinear hyperbolic partial differential equations.

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