scholarly journals Subdivision Collocation Method for One-Dimensional Bratu’s Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Ghulam Mustafa ◽  
Syeda Tehmina Ejaz ◽  
Sabila Kouser ◽  
Shafqat Ali ◽  
Muhammad Aslam
Keyword(s):  
Boundary Value Problem ◽  
Collocation Method ◽  
Boundary Value ◽  
Accurate Solution ◽  
Subdivision Scheme ◽  
Algebraic Equations ◽  
Physical Sciences ◽  
One Dimensional ◽  
Bratu’S Problem ◽  
Approximating Subdivision Scheme

The purpose of this article is to employ the subdivision collocation method to resolve Bratu’s boundary value problem by using approximating subdivision scheme. The main purpose of this researcher is to explore the application of subdivision schemes in the field of physical sciences. Our approach converts the problem into a set of algebraic equations. Numerical approximations of the solution of the problem and absolute errors are compared with existing methods. The comparison shows that the proposed method gives a more accurate solution than the existing methods.

scholarly journals Uniqueness and stability of solutions for a type of parabolic boundary value problem

1989 ◽  
Vol 12 (4) ◽  
pp. 735-739
Author(s):  
Enrique A. Gonzalez-Velasco
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problem ◽  
Nonnegative Solution ◽  
Boundary Value ◽  
Stability Of Solutions ◽  
General Boundary Conditions ◽  
Boundary Values ◽  
Parabolic Boundary ◽  
One Dimensional ◽  
The One

We consider a boundary value problem consisting of the one-dimensional parabolic equationgut=(hux)x+q, where g, h and q are functions of x, subject to some general boundary conditions. By developing a maximum principle for the boundary value problem, rather than the equation, we prove the uniqueness of a nonnegative solution that depends continuously on boundary values.

scholarly journals Pairs of nodal solutions for a Minkowski-curvature boundary value problem in a ball

2019 ◽  
Vol 21 (02) ◽  
pp. 1850006 ◽  
Author(s):  
Alberto Boscaggin ◽  
Maurizio Garrione
Keyword(s):  
Boundary Value Problem ◽  
Neumann Problem ◽  
Boundary Value ◽  
Periodic Problem ◽  
Nodal Solutions ◽  
Shooting Technique ◽  
One Dimensional ◽  
Dimensional Equation

By using a shooting technique, we prove that the quasilinear boundary value problem [Formula: see text] where [Formula: see text] is a ball and [Formula: see text], has more and more pairs of nodal solutions on growing of the parameter [Formula: see text]. The radial Neumann problem and the periodic problem for the corresponding one-dimensional equation are considered, as well.

A Discretization Approach to Modeling Capacitive MEMS Filters

2007 ◽  
Author(s):  
Bashar K. Hammad ◽  
Ali H. Nayfeh ◽  
Eihab Abdel-Rahman
Keyword(s):  
Boundary Value Problem ◽  
Closed Form ◽  
Natural Frequencies ◽  
Multiple Scales ◽  
Boundary Value ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Nonlinear Odes ◽  
Global Mode ◽  
Wide Range

We present a reduced-order model and closed-form expressions describing the response of a micromechanical filter made up of two clamped-clamped microbeam capacitive resonators coupled by a weak microbeam. The model accounts for geometrical and electrical nonlinearities as well as the coupling between them. It is obtained by discretizing the distributed-parameter system using the Galerkin procedure. The basis functions are the linear undamped global mode shapes of the unactuated filter. Closed-form expressions for these mode shapes and the coressponding natural frequencies are obtained by formulating a boundary-value problem (BVP) that is composed of five equations and twenty boundary conditions. This problem is transformed into solving a system of twenty linear homogeneous algebraic equations for twenty constants and the natural frequencies. We predict the deflection and the voltage at which the static pull-in occurs by solving another boundary-value problem (BVP). We also solve an eigenvalue problem (EVP) to determine the two natural frequencies delineating the bandwidth of the actuated filter. Using the method of multiple scales, we determine four first-order nonlinear ODEs describing the amplitudes and phases of the modes. We found a good agreement between the results obtained using our model and the published experimental results. We found that the filter can be tuned to operate linearly for a wide range of input signal strengths by choosing a DC voltage that makes the effective nonlinearities vanish.

Sign in / Sign up

Export Citation Format

Share Document