In the last years, the theory of numerical methods for system of non-stiff and stiff ordinary differential equations has reached a certain maturity. So, there are many excellent codes which are based on Runge–Kutta methods, linear multistep methods, Obreshkov methods, hybrid methods or general linear methods. Although these methods have good accuracy and desirable stability properties such as A...

case presentation the patient was a 65-year-old female with sps diagnosed 1 year before. assessments were performed, such as range of motion, muscle strength, pain, balance, and functional mobility. she had shoulder pain, with a score of 5/10 on the numerical pain rating scale for both shoulders. moreover, her muscle strength was impaired. although the patient could not maintain an upright posi...

Some new higher algebraic order symmetric various-step methods are introduced. For these methods a direct formula for the computation of the phase-lag is given. Basing on this formula, calculation of free parameters is performed to minimize the phase-lag. An explicit symmetric multistep method is presented. This method is of higher algebraic order and is fitted both exponentially and trigonomet...

We present a new strategy for solving stiff ODEs with explicit methods. By adaptively taking a small number of stabilizing small explicit time steps when necessary, a stiff ODE system can be stabilized enough to allow for time steps much larger than what is indicated by classical stability analysis. For many stiff problems the cost of the stabilizing small time steps is small, so the improvemen...

We develop the methodology of multi-adaptive time-stepping for stiff problems. The new algorithm is based on adaptively stabilized fixed point iteration on time slabs and a new method for the recursive construction of time slabs. Numerical examples are given for a series of well-known stiff and non-stiff test problems.

There are many laws stating the behavior of the physical world involves quantities which are changing with respect to another quantities and the mathematical expressions of such laws are differential equations. There are numbers of problems of various fields like science, engineering-technology, social science etc. involves differential equations. The researchers have developed many analytical ...