The immersed boundary (IB) method is an algorithm for simulating elastic structures immersed in a fluid. The IB method can be used, for example, to simulate blood flow in the heart. Even running on supercomputers, software implementations require on the order of seven CPU-days to simulate one heart beat. The IB method has significant, inherent, fine-grain parallelism available. This parallelism...

The method of upper and lower solutions and quasilinearization for nonlinear singular equations of the type −x(t) + λx(t) = f(t, x(t)), t ∈ (0, 1), subject to nonlocal three-point boundary conditions x(0) = δx(η), x(1) = 0, 0 < η < 1, are developed. Existence of a C1 positive solution is established. A monotone sequence of solutions of linear problems converging uniformly and rapidly to a solut...

Pseudospectral collocation is employed for the numerical solution of nonlinear two-point boundary value problems with separated end conditions. Second-order finite difference schemes are used as preconditioners for the spectral calculation, and a solution of the discretized equations is obtained using versions of the defect correction principle. The method and a variant based on an adaptive gri...

In this paper, vibration analysis of multiple-stepped Bernoulli-Euler and Timoshenko beams carrying point masses is presented analytically for various boundary conditions. Each attached element is considered to have both translational and rotational inertias. The method of solution is “transfer matrix method” which is based on the changes in the vibration modes at the vicinity of any discontinu...

In this research, second order linear two-point boundary value problems are treated using new method based on hybrid cubic B-spline. The values of the free parameter,Gamma , chosen via optimization. parameter plays an important role in giving accurate results. Optimization is carried out. This tested four examples and a comparison with B-spline, trigonometric B-spline extended methods has been ...

In this paper we develop an iterative numerical method based on Bernstein splines for solving two-point boundary problems associated to differential equations of fractional order $\alpha\in\left( 0,1\right) $. The convergence the is proved by providing error estimate and it tested a example.

in this paper we study the boundary layer problems in which boundary conditions are non-local. here we try to find the necessary conditions by the help of fundamental solution to the given adjoint equation. by getting help from these conditions, at first the boundary condition is changed from non-local to local. the main aim of this paper is to identify the location of the boundary layer. in ot...

in this paper, a chebyshev finite difference method has been proposed in order to solvenonlinear two-point boundary value problems for second order nonlinear differentialequations. a problem arising from chemical reactor theory is then considered. the approachconsists of reducing the problem to a set of algebraic equations. this method can be regardedas a non-uniform finite difference scheme. t...