On The Existence Of Multiple Solutions Of A Class Of Second-order Nonlinear Two-point Boundary Value Problems

Shivanian, Elyas; Abdolrazaghi, Fatemeh

doi:10.22436/jmcs.014.02.02

Cited by 3 publications

(1 citation statement)

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“…• Throw in additional stages, off-step points, super-future points and like (see [1,7,8,9,11]). This leads to different kind of the linear methods.…”

Section: Introductionmentioning

confidence: 99%

P-stable Hybrid Super-implicit Methods For Periodic Initial Value Problems

Khalsaraei¹,

Molayi²

2015

J. Math. Computer Sci.

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This paper deals with a class of symmetric (hybrid) P-stable methods for the numerical solution of special second order initial value problems (IVPs). For linear multistep methods, Lambert and Watson [5], had shown that a P-stable method is necessarily implicit and that the maximum order attainable by a P -stable method is at most two. P-stability is important in the case of 'periodic stiffness' as it is termed by Lambert and Watson [5], that is, when the solution consists of an oscillation of moderate frequency with a high frequency oscillation of small amplitude superimposed. In order to overcome the order-barrier on linear multistep P-stable methods, we developed a new type of implicit formulas of linear multistep methods. The formulas, which we call to be hybrid super-implicit, are of more implicitness than the socalled implicit formulas in the sense that they require the knowledge of functions not only at the past and present time-step but also at the future ones. In the cases when the right hand side of IVP is very complex, the super-implicit methods are preferred. Also, we have used off-step points which allow us to derive Pstable schemes of high order. We report numerical experiments to illustrate the accuracy and implementation aspects of this class of methods.

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“…• Throw in additional stages, off-step points, super-future points and like (see [1,7,8,9,11]). This leads to different kind of the linear methods.…”

Section: Introductionmentioning

confidence: 99%