Non-homogeneous boundary value problems for some KdV-type equations on a finite interval: A numerical approach

2021 ◽  
Vol 96 ◽  
pp. 105669
Author(s):  
Juan Carlos Muñoz Grajales
Keyword(s):  
Boundary Value Problems ◽  
Finite Interval ◽  
Boundary Value ◽  
Numerical Approach ◽  
Kdv Type Equations

scholarly journals Solving Nonlinear Fourth-Order Boundary Value Problems Using a Numerical Approach: (m+1)th-Step Block Method

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Oluwaseun Adeyeye ◽  
Zurni Omar
Keyword(s):  
Boundary Value Problems ◽  
Fourth Order ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Numerical Approach ◽  
Squeezing Flow ◽  
Nonlinear Boundary Value Problems ◽  
Block Method ◽  
Nonlinear Boundary Value ◽  
Improved Accuracy

Nonlinear boundary value problems (BVPs) are more tedious to solve than their linear counterparts. This is observed in the extra computation required when determining the missing conditions in transforming BVPs to initial value problems. Although a number of numerical approaches are already existent in literature to solve nonlinear BVPs, this article presents a new block method with improved accuracy to solve nonlinear BVPs. A m+1th-step block method is developed using a modified Taylor series approach to directly solve fourth-order nonlinear boundary value problems (BVPs) where m is the order of the differential equation under consideration. The schemes obtained were combined to simultaneously produce solution to the fourth-order nonlinear BVPs at m+1 points iteratively. The derived block method showed improved accuracy in comparison to previously existing authors when solving the same problems. In addition, the suitability of the m+1th-step block method was displayed in the solution for magnetohydrodynamic squeezing flow in porous medium.

scholarly journals Positive Solutions of the One-Dimensional p-Laplacian with Nonlinearity Defined on a Finite Interval

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Ruyun Ma ◽  
Chunjie Xie ◽  
Abubaker Ahmed
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Finite Interval ◽  
Boundary Value ◽  
Quadrature Method ◽  
One Dimensional ◽  
Existence And Multiplicity ◽  
The One ◽  
Multiplicity Of Positive Solutions

We use the quadrature method to show the existence and multiplicity of positive solutions of the boundary value problems involving one-dimensional p-Laplacian u′t|p−2u′t′+λfut=0, t∈0,1, u(0)=u(1)=0, where p∈(1,2], λ∈(0,∞) is a parameter, f∈C1([0,r),[0,∞)) for some constant r>0, f(s)>0 in (0,r), and lims→r-(r-s)p-1f(s)=+∞.

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