Comment on the paper “A class of methods based on non-polynomial spline functions for the solution of a special fourth-order boundary-value problems with engineering applications”

2007 ◽  
Vol 186 (2) ◽  
pp. 1572-1580 ◽  
Author(s):  
J. Rashidinia ◽  
R. Jalilian ◽  
R. Mohammadi
Keyword(s):  
Boundary Value Problems ◽  
Fourth Order ◽  
Boundary Value ◽  
Polynomial Spline ◽  
Spline Functions ◽  
Engineering Applications

scholarly journals Spline Methods for a Class of Singularly Perturbed Boundary Value Problems

2013 ◽  
Vol 2 (1) ◽  
pp. 1-10
Author(s):  
O.M Ogunlaran ◽  
O.A Taiwo
Keyword(s):  
Numerical Methods ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Spline Function ◽  
Boundary Value ◽  
Polynomial Spline ◽  
Second Order ◽  
Singularly Perturbed ◽  
Uniform Grid ◽  
Numerical Examples

In this paper, we develop numerical methods based on a non-polynomial spline function with uniform grid for solving certain class of singularly perturbed boundary value problems. The proposed methods are second-order and fourth-order accurate. Numerical examples are provided to demonstrate the efficiency of the proposed methods.

On Solvability and Well-Posedness of Boundary Value Problems for Nonlinear Hyperbolic Equations of the Fourth Order

2008 ◽  
Vol 15 (3) ◽  
pp. 555-569
Author(s):  
Tariel Kiguradze
Keyword(s):  
Hyperbolic Equation ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Hyperbolic Equations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Nonlinear Hyperbolic Equation ◽  
Well Posedness ◽  
Nonlinear Hyperbolic Equations ◽  
Right Hand

Abstract In the rectangle Ω = [0, a] × [0, b] the nonlinear hyperbolic equation 𝑢(2,2) = 𝑓(𝑥, 𝑦, 𝑢) with the continuous right-hand side 𝑓 : Ω × ℝ → ℝ is considered. Unimprovable in a sense sufficient conditions of solvability of Dirichlet, Dirichlet–Nicoletti and Nicoletti boundary value problems are established.

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