scholarly journals On the parametrization of nonlinear boundary value problems with nonlinear boundary conditions

2011 ◽  
Vol 12 (2) ◽  
pp. 209
Author(s):  
K. Marynets
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Conditions ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value

scholarly journals Coupled System of Boundary Value Problems by Galerkin Method with Cubic B-Splines

2019 ◽  
Vol 128 ◽  
pp. 09008
Author(s):  
K.N.S Kasi Viswanadham
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Coupled System ◽  
Basis Functions ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value ◽  
Linear And Nonlinear

Coupled system of second order linear and nonlinear boundary value problems occur in various fields of Science and Engineering including heat and mass transfer. In the formulation of the problem, any one of 81 possible types of boundary conditions may occur. These 81 possible boundary conditions are written as a combination of four boundary conditions. To solve a coupled system of boundary value problem with these converted boundary conditions, a Galerkin method with cubic Bsplines as basis functions has been developed. The basis functions have been redefined into a new set of basis functions which vanish on the boundary. The nonlinear boundary value problems are solved with the help of quasilinearization technique. Several linear and nonlinear boundary value problems are presented to test the efficiency of the proposed method and found that numerical results obtained by the present method are in good agreement with the exact solutions available in the literature.

scholarly journals An efficient numerical approach for solving two-point fractional order nonlinear boundary value problems with Robin boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hyunju Kim ◽  
Junseo Lee ◽  
Bongsoo Jang
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Fractional Order ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Robin Boundary Conditions ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value ◽  
And Performance ◽  
Robin Boundary

AbstractThis article proposes new strategies for solving two-point Fractional order Nonlinear Boundary Value Problems (FNBVPs) with Robin Boundary Conditions (RBCs). In the new numerical schemes, a two-point FNBVP is transformed into a system of Fractional order Initial Value Problems (FIVPs) with unknown Initial Conditions (ICs). To approximate ICs in the system of FIVPs, we develop nonlinear shooting methods based on Newton’s method and Halley’s method using the RBC at the right end point. To deal with FIVPs in a system, we mainly employ High-order Predictor–Corrector Methods (HPCMs) with linear interpolation and quadratic interpolation (Nguyen and Jang in Fract. Calc. Appl. Anal. 20(2):447–476, 2017) into Volterra integral equations which are equivalent to FIVPs. The advantage of the proposed schemes with HPCMs is that even though they are designed for solving two-point FNBVPs, they can handle both linear and nonlinear two-point Fractional order Boundary Value Problems (FBVPs) with RBCs and have uniform convergence rates of HPCMs, $\mathcal{O}(h^{2})$ O ( h 2 ) and $\mathcal{O}(h^{3})$ O ( h 3 ) for shooting techniques with Newton’s method and Halley’s method, respectively. A variety of numerical examples are demonstrated to confirm the effectiveness and performance of the proposed schemes. Also we compare the accuracy and performance of our schemes with another method.

Sign in / Sign up

Export Citation Format

Share Document