scholarly journals Subdivision Schemes Based Collocation Algorithms for Solution of Fourth Order Boundary Value Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-18 ◽  
Author(s):  
Syeda Tehmina Ejaz ◽  
Ghulam Mustafa ◽  
Faheem Khan
Keyword(s):  
Mathematical Modeling ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Boundary Value ◽  
Engineering Systems ◽  
Subdivision Schemes ◽  
Load Bearing ◽  
Robotic Arms ◽  
Numerical Examples ◽  
Comparison Of The Results

We present two collocation algorithms based on interpolating and approximating subdivision schemes for the solution of fourth order boundary value problems arising in the mathematical modeling of viscoelastic, and inelastic flows, deformation of beams, arches, and load bearing members like street lights and robotic arms in multipurpose engineering systems. Numerical examples are given to illustrate the algorithms. We conclude that approximating schemes based collocation algorithms give better solution than interpolating schemes based collocation algorithms. Main purpose of this paper is to explore and seek the applications of interpolating and approximating subdivision schemes in the field of boundary value problems along with intrinsic comparison of the results obtained by algorithms based on these schemes. A comparison with other approaches of this type of boundary value problems in order to see the advantages of the proposed methods is also given.

scholarly journals Exponential spline approach for the solution of fourth order obstacle boundary value problems

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 993-1004 ◽  
Author(s):  
Arshad Khan ◽  
Shilpi Bisht
Keyword(s):  
Boundary Value Problems ◽  
Fourth Order ◽  
Boundary Value ◽  
Contact Problems ◽  
The Other ◽  
Numerical Illustration ◽  
Quintic Spline ◽  
Numerical Examples ◽  
Exponential Spline ◽  
Present Technique

An exponential quintic spline technique at mid knots is developed for approximating the solution of system of fourth order boundary value problems associated with obstacle, unilateral and contact problems. The present technique gives a class of methods of order two, four and six. Two numerical examples are considered for the numerical illustration of the proposed method. It is shown that the method developed in this paper is more efficient than the other finite difference, collocation and spline methods.

scholarly journals Numerical Solution of Two-Point Boundary Value Problems by Interpolating Subdivision Schemes

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Ghulam Mustafa ◽  
Syeda Tehmina Ejaz
Keyword(s):  
Numerical Solution ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Point Boundary ◽  
Approximation Properties ◽  
Third Order ◽  
Continuous Solutions ◽  
Subdivision Schemes ◽  
Numerical Examples

A numerical interpolating algorithm of collocation is formulated, based on 8-point binary interpolating subdivision schemes for the generation of curves, to solve the two-point third order boundary value problems. It is observed that the algorithm produces smooth continuous solutions of the problems. Numerical examples are given to illustrate the algorithm and its convergence. Moreover, the approximation properties of the collocation algorithm have also been discussed.

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.

EXISTENCE THEOREMS OF POSITIVE SOLUTIONS FOR FOURTH-ORDER FOUR-POINT BOUNDARY VALUE PROBLEMS

2004 ◽  
Vol 02 (01) ◽  
pp. 71-85 ◽  
Author(s):  
YUJI LIU ◽  
WEIGAO GE
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fourth Order ◽  
Existence Theorems ◽  
Boundary Value ◽  
Growth Conditions ◽  
Point Boundary ◽  
Order Ordinary Differential Equation ◽  
Order Four

In this paper, we study four-point boundary value problems for a fourth-order ordinary differential equation of the form [Formula: see text] with one of the following boundary conditions: [Formula: see text] or [Formula: see text] Growth conditions on f which guarantee existence of at least three positive solutions for the problems (E)–(B1) and (E)–(B2) are imposed.

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