Comparison of Multiplier and Quasilinearization Methods

1975 ◽  
Vol 14 (4) ◽  
pp. 385-391 ◽  
Author(s):  
Alejandro V. Levy ◽  
Antonio Montalvo
Keyword(s):  
Quasilinearization Methods

Quasilinearization Methods for Nonlinear Parabolic Equations with Functional Dependence

2002 ◽  
Vol 9 (3) ◽  
pp. 431-448
Author(s):  
A. Bychowska
Keyword(s):  
Cauchy Problem ◽  
Parabolic Equations ◽  
Unknown Function ◽  
Functional Dependence ◽  
Nonlinear Parabolic Equations ◽  
Quasilinearization Method ◽  
Convergence Theorems ◽  
Nonlinear Parabolic ◽  
Quasilinearization Methods ◽  
Derivatives Of

Abstract We consider a Cauchy problem for nonlinear parabolic equations with functional dependence. We prove convergence theorems for a general quasilinearization method in two cases: (i) the Hale functional acting only on the unknown function, (ii) including partial derivatives of the unknown function.

Quasilinearization Methods for Proving Inequalities

1993 ◽  
pp. 669-679
Author(s):  
D. S. Mitrinović ◽  
J. E. Pečarić ◽  
A. M. Fink
Keyword(s):  
Quasilinearization Methods

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.

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