scholarly journals Non-polynomial Cubic Spline Method for the Solution of Second-order Linear Hyperbolic Equation

2021 ◽  
Vol 20 ◽  
pp. 301-308
Author(s):  
Nazan Çağlar
Keyword(s):  
Taylor Expansion ◽  
Hyperbolic Equations ◽  
Polynomial Spline ◽  
Second Order ◽  
Spline Method ◽  
Linear Hyperbolic Equation ◽  
Time Direction ◽  
Order Linear ◽  
Level Method ◽  
Linear Hyperbolic Equations

Second-order linear hyperbolic equations are solved by using a new three level method based on nonpolynomial spline in the space direction and Taylor expansion in the time direction. Numerical results reveal that three level method based on non-polynomial spline is implemented and effective

On the Correctness of the Dirichlet Problem in a Characteristic Rectangle for Fourth Order Linear Hyperbolic Equations

1999 ◽  
Vol 6 (5) ◽  
pp. 447-470
Author(s):  
T. Kiguradze
Keyword(s):  
Dirichlet Problem ◽  
Hyperbolic Equation ◽  
Fourth Order ◽  
Trivial Solution ◽  
Hyperbolic Equations ◽  
Homogeneous Problem ◽  
Linear Hyperbolic Equation ◽  
Order Linear ◽  
Linear Hyperbolic Equations

Abstract It is proved that the Dirichlet problem is correct in the characteristic rectangle 𝐷𝑎𝑏 = [0, 𝑎] × [0, 𝑏] for the linear hyperbolic equation with the summable in 𝐷𝑎𝑏 coefficients 𝑝0, 𝑝1, 𝑝2, 𝑝3 and 𝑞 if and only if the corresponding homogeneous problem has only the trivial solution. The effective and optimal in some sense restrictions on 𝑝0, 𝑝1, 𝑝2 and 𝑝3 guaranteeing the correctness of the Dirichlet problem are established.

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