scholarly journals A NEW THIRD ORDER EXPONENTIALLY FITTED DISCRETIZATION FOR THE SOLUTION OF NON-LINEAR TWO POINT BOUNDARY VALUE PROBLEMS ON A GRADED MESH

2020 ◽  
Vol 10 (5) ◽  
pp. 1741-1770
Author(s):  
R. K. Mohanty ◽  
◽  
Geetan Manchanda ◽  
Gunjan Khurana ◽  
Arshad Khan ◽  
...  
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Graded Mesh ◽  
Non Linear ◽  
Exponentially Fitted

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

scholarly journals Solving nonlinear third-order three-point boundary value problems by boundary shape functions methods

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ji Lin ◽  
Yuhui Zhang ◽  
Chein-Shan Liu
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Initial Conditions ◽  
Boundary Value ◽  
Accurate Solution ◽  
Point Boundary ◽  
Third Order ◽  
Boundary Shape ◽  
Free Function ◽  
New Algorithms

AbstractFor nonlinear third-order three-point boundary value problems (BVPs), we develop two algorithms to find solutions, which automatically satisfy the specified three-point boundary conditions. We construct a boundary shape function (BSF), which is designed to automatically satisfy the boundary conditions and can be employed to develop new algorithms by assigning two different roles of free function in the BSF. In the first algorithm, we let the free functions be complete functions and the BSFs be the new bases of the solution, which not only satisfy the boundary conditions automatically, but also can be used to find solution by a collocation technique. In the second algorithm, we let the BSF be the solution of the BVP and the free function be another new variable, such that we can transform the BVP to a corresponding initial value problem for the new variable, whose initial conditions are given arbitrarily and terminal values are determined by iterations; hence, we can quickly find very accurate solution of nonlinear third-order three-point BVP through a few iterations. Numerical examples confirm the performance of the new algorithms.

scholarly journals On the Solvability of Nonlinear Third-Order Two-Point Boundary Value Problems

Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 62
Author(s):  
Ravi P. Agarwal ◽  
Petio S. Kelevedjiev ◽  
Todor Z. Todorov
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Barrier Strips

Under barrier strips type assumptions we study the existence of C 3 [ 0 , 1 ] —solutions to various two-point boundary value problems for the equation x ‴ = f ( t , x , x ′ , x ″ ) . We give also some results guaranteeing positive or non-negative, monotone, convex or concave solutions.

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