scholarly journals The method of generalized quasilinearization and higher order of convergence for second-order boundary value problems

2006 ◽  
pp. 569-582
Author(s):  
Ramzi S. N. Alsaedi
Keyword(s):  
Boundary Value Problems ◽  
Order Of Convergence ◽  
Boundary Value ◽  
Higher Order ◽  
Second Order

scholarly journals An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Eman S. Alaidarous ◽  
Malik Zaka Ullah ◽  
Fayyaz Ahmad ◽  
A.S. Al-Fhaid
Keyword(s):  
Boundary Value Problems ◽  
Decomposition Method ◽  
Order Of Convergence ◽  
Nonlinear Differential Equations ◽  
Boundary Value ◽  
Higher Order ◽  
Critical Parameters ◽  
Computational Performance ◽  
Highly Nonlinear ◽  
Quasilinearization Methods

In this research paper, we present higher-order quasilinearization methods for the boundary value problems as well as coupled boundary value problems. The construction of higher-order convergent methods depends on a decomposition method which is different from Adomain decomposition method (Motsa and Sibanda, 2013). The reported method is very general and can be extended to desired order of convergence for highly nonlinear differential equations and also computationally superior to proposed iterative method based on Adomain decomposition because our proposed iterative scheme avoids the calculations of Adomain polynomials and achieves the same computational order of convergence as authors have claimed in Motsa and Sibanda, 2013. In order to check the validity and computational performance, the constructed iterative schemes are also successfully applied to bifurcation problems to calculate the values of critical parameters. The numerical performance is also tested for one-dimension Bratu and Frank-Kamenetzkii equations.

scholarly journals Solving Integro-Differential Boundary Value Problems Using Sinc-Derivative Collocation

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1637
Author(s):  
Kenzu Abdella ◽  
Glen Ross
Keyword(s):  
Numerical Methods ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Numerical Integration ◽  
Collocation Method ◽  
Boundary Value ◽  
Numerical Differentiation ◽  
Higher Order ◽  
Second Order ◽  
Collocation Approach

In this paper, the sinc-derivative collocation approach is used to solve second order integro-differential boundary value problems. While the derivative of the unknown variables is interpolated using sinc numerical methods, the desired solution and the integral terms are evaluated through numerical integration and all higher order derivatives are approximated through successive numerical differentiation. Suitable transformations are used to reduce non-homogeneous boundary conditions to homogeneous. Comparison of the proposed method with different approaches that were previously considered in the literature is carried out in order to test its accuracy and efficiency. The results show that the sinc-derivative collocation method performs well.

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