scholarly journals Wendroff type inequalities for nonlinear hyperbolic equations

2001 ◽  
Vol 32 (4) ◽  
pp. 327-333
Author(s):  
Wen Rong Li ◽  
Sui Sun Cheng
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Initial Value Problems ◽  
Hyperbolic Equations ◽  
Hyperbolic Partial Differential Equations ◽  
Nonlinear Hyperbolic Equations ◽  
Initial Value ◽  
Partial Differential

Several Wendroff type inequalities are derived, and applications to characteristic initial value problems involving hyperbolic partial differential equations are illustrated.

scholarly journals Functionally Fitted Block Method for Solving the General Oscillatory Second-Order Initial Value Problems and Hyperbolic Partial Differential Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
S. N. Jator ◽  
F. F. Ngwane ◽  
N. O. Kirby
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Initial Value Problems ◽  
Second Order ◽  
Hyperbolic Partial Differential Equations ◽  
Fixed Frequency ◽  
Block Method ◽  
Initial Value ◽  
Partial Differential ◽  
Predictor Corrector

We present a block hybrid functionally fitted Runge–Kutta–Nyström method (BHFNM) which is dependent on the stepsize and a fixed frequency. Since the method is implemented in a block-by-block fashion, the method does not require starting values and predictors inherent to other predictor-corrector methods. Upon deriving our method, stability is illustrated, and it is used to numerically solve the general second-order initial value problems as well as hyperbolic partial differential equations. In doing so, we demonstrate the method’s relative accuracy and efficiency.

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.

Computing experience with hyperbolic partial differential equations

1971 ◽  
Vol 323 (1553) ◽  
pp. 263-270 ◽  
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Differential Equations ◽  
Hyperbolic Equations ◽  
Artificial Viscosity ◽  
Hyperbolic Partial Differential Equations ◽  
Nonlinear Hyperbolic Equations ◽  
Particle In Cell ◽  
Large Numbers ◽  
Eulerian Mesh

Three methods of integrating nonlinear hyperbolic equations are considered, namely the characteristic, mesh finite-difference and particle-in-cell techniques. In particular, a practical characteristic code for problems with large numbers of discontinuities is described, and developments in the use of artificial viscosity terms are outlined. The incorporation of certain particle-in-cell features into Eulerian mesh methods is also illustrated.

Oscillation of Neural Type Nonlinear Impulsive Hyperbolic Equations with Several Delays

2013 ◽  
Vol 275-277 ◽  
pp. 843-847
Author(s):  
Li Xiao ◽  
Ji Chen Yang ◽  
Guang Jie Liu ◽  
An Ping Liu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Hyperbolic Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Hyperbolic Partial Differential Equations ◽  
Partial Differential ◽  
Several Delays ◽  
Oscillatory Properties

In this paper, oscillatory properties of solutions for neutral type nonlinear impulsive hyperbolic partial differential equations with several delays are investigated and a series of sufficient conditions for oscillation of the equations are established.

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