In this paper, a nonlinear stiff differential equation is solved by using the Rosenbrock iterative method, modified homotpy analysis method and power series method. The approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relations. Some numerical examples are studied to demonstrate the accuracy of the presented meth...

For many systems of differential equations modeling problems in science and engineering, there are often natural splittings of the right hand side into two parts, one of which is non-stiff or mildly stiff, and the other part is stiff. Such systems can be efficiently treated by a class of implicit-explicit (IMEX) diagonally implicit multistage integration methods (DIMSIMs), where the stiff part ...

In this article we present a new family of high order accurate Arbitrary Lagrangian-Eulerian one-step WENO finite volume schemes for the solution of stiff hyperbolic balance laws. High order accuracy in space is obtained with a standard WENO reconstruction algorithm and high order in time is obtained using the local space-time discontinuous Galerkinmethod recently proposed in [20]. In the Lagra...

Runge-Kutta methods are an important family of implicit and explicit iterative methods used for the approximation of solutions of ordinary differential equations. Explicit RungeKutta methods are unsuitable for the solution of stiff equations as their region of stability is small. Stiff equation is a differential equation for which certain numerical methods for solving the equation are numerical...

Asymptotic behaviour of eigenvalues and eigenfunctions of a stiff problem is described in the case of the fourth-order ordinary differential operator. Considering the stiffness coefficient that depends on a small parameter ε and vanishes as ε → 0 on a subinterval, we prove the existence of low and high frequency resonance vibrations. The low frequency vibrations admit the power series expansion...

In this article we propose a new class of finite volume schemes of arbitrary accuracy in space and time for systems of hyperbolic balance laws with stiff source terms. The new class of schemes is based on a three stage procedure. First, in order to achieve high order accuracy in space, a nonlinear weighted essentially non-oscillatory reconstruction procedure is applied to the cell averages at t...

A component-based methodology to derive parallel stiff Ordinary Differential Equation (ODE) solvers for multicomputers is presented. The methodology allows the exploitation of the multilevel parallelism of this kind of numerical algorithms and the particular structure of ODE systems by using parallel linear algebra modules. The approach furthers the reusability of the design specifications and ...

The propensity of stem cells to specify and commit to a particular lineage program is guided by dynamic biophysical and biochemical signals that are temporally regulated. However, most in vitro studies rely on "snapshots" of cell state under static conditions. Here we asked whether changing the biophysical aspects of the substrate could modulate the degree of mesenchymal stem cell (MSC) lineage...

Stabilized or Chebyshev explicit methods have been widely used in the past to solve stiff ordinary differential equations. Making use of special properties of Chebyshev-like polynomials, these methods have favorable stability properties compared to standard explicit methods while remaining explicit. A new class of such methods, called ROCK, introduced in [Numer. Math., 90, 1-18, 2001] has recen...

The mechanical property of extracellular matrix and cell-supporting substrates is known to modulate neuronal growth, differentiation, extension and branching. Here we show that substrate stiffness is an important microenvironmental cue, to which mouse hippocampal neurons respond and integrate into synapse formation and transmission in cultured neuronal network. Hippocampal neurons were cultured...