Related papers: Investigation on the Shooting Method Ability to So…
This article presents an alternative approach to finite elements for modeling and analyzing 3D static mooring lines using string theory and the shooting method (SM) to solve two-point boundary value problems (TPBVPs) for 3D nonlinear static…
This paper presents a novel shooting method for solving two-point boundary value problems for second order ordinary differential equations. The method works as follows: first, a guess for the initial condition is made and an integration of…
Boundary value problems in ODEs arise in modelling many physical situations from microscale to mega scale. Such two-point boundary value problems (BVPs) are complex and often possess no analytical closed form solutions. So, one has to rely…
We use the standard multiple shooting method to solve a linear two point boundary-value problem. To ensure that the solution obtained by combining the partial solutions is continuous and satisfies the boundary conditions, we have to solve a…
The Kirchhoff model describes the statics and dynamics of thin rods within the approximations of the linear elasticity theory. In this paper we develop a method, based on a shooting technique, to find equilibrium configurations of finite…
A high-performance shooting algorithm is developed to compute time-periodic solutions of the free-surface Euler equations with spectral accuracy in double and quadruple precision. The method is used to study resonance and its effect on…
This paper presents an adaptive multiple-shooting method to solve stochastic multi-point boundary value problems. The heuristic to choose the shooting points is based on separating the effects of drift and diffusion terms and comparing the…
In this paper, we propose two approaches to apply boundary conditions for bond-based peridynamic models. There has been in recent years a renewed interest in the class of so-called non-local models, which include peridynamic models, for the…
A non-conventional shape optimization approach is introduced to address the identification of an obstacle immersed in a fluid described by the Stokes equation within a larger bounded domain, relying on boundary measurements on the…
The conventional no-slip boundary condition leads to a non-integrable stress singularity at a moving contact line. This makes numerical simulations challenging, especially when capillary effects are essential for the dynamics of the flow.…
The model problem of a plane angle for a second-order elliptic system subject to Dirichlet, mixed, and Neumann boundary conditions is analyzed. For each boundary condition, the existence of solutions of the form $r^\lambda v$ is reduced to…
Recently, a flexible and stable algorithm was introduced for the computation of 2D unstable manifolds of periodic solutions to systems of ordinary differential equations. The main idea of this approach is to represent orbits in this…
We present a systematic method for exactly enforcing Dirichlet, Neumann, and Robin type conditions on general quadrilateral domains with arbitrary curved boundaries. Our method is built upon exact mappings between general quadrilateral…
We derive and analyse well-posed boundary conditions for the linear shallow water wave equation. The analysis is based on the energy method and it identifies the number, location and form of the boundary conditions so that the initial…
The shooting method is used to solve a boundary value problem with separated and explicit constraints. To obtain approximations of an unknown initial values there are considered arguments based on the adjoint differential system attached to…
This paper aims to solve the equations of geometrically exact 3D nonlinear Cosserat static rods under large displacements with a mesh free alternative method to finite elements: the shooting method. One of the main goal of the work…
We propose methods that augment existing numerical schemes for the simulation of hyperbolic balance laws with Dirichlet boundary conditions to allow for the simulation of a broad class of differential algebraic conditions. Our approach is…
Two-point boundary value problems for a discrete Ermakov-Painlev\'e II equation are analysed by means of topological methods. In addition, an alternative variational approach is detailed. Existence of solutions is established for…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
This article proposes new strategies for solving two-point Fractional order Nonlinear Boundary Value Problems(FN-BVPs) with Robin Boundary Conditions(RBCs). In the new numerical schemes, a two-point FNBVP is transformed into a system of…