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 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 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.

scholarly journals Multiple Solutions for a Class of Nonlinear Fourth-Order Boundary Value Problems

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1989
Author(s):  
Longfei Lin ◽  
Yansheng Liu ◽  
Daliang Zhao
Keyword(s):  
Boundary Value Problems ◽  
Fourth Order ◽  
Multiple Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
The Other ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Special Cone

This paper is concerned with multiple solutions for a class of nonlinear fourth-order boundary value problems with parameters. By constructing a special cone and applying fixed point index theory, the multiple solutions for the considered systems are obtained under some suitable assumptions. The main feature of obtained solutions (u(t),v(t)) is that the solution u(t) is positive, and the other solution v(t) may change sign. Finally, two examples with continuous function f1 being positive and f2 being semipositone are worked out to illustrate the main results.

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