EXPONENTIALLY AND TRIGONOMETRICALLY FITTED EXPLICIT ADVANCED STEP-POINT (EAS) METHODS FOR INITIAL VALUE PROBLEMS WITH OSCILLATING SOLUTIONS

2003 ◽  
Vol 14 (02) ◽  
pp. 175-184 ◽  
Author(s):  
G. PSIHOYIOS ◽  
T. E. SIMOS
Keyword(s):  
Numerical Solution ◽  
Initial Value Problems ◽  
Initial Value ◽  
Numerical Examples ◽  
Oscillating Solutions ◽  
Exponentially Fitted ◽  
Predictor Corrector ◽  
Area Of Application

In this paper, an exponentially fitted and trigonometrically fitted predictor–corrector class of methods is developed. These methods represent a totally new area of application for the explicit advanced step-point or EAS methods developed by Psihoyios and Cash. Numerical examples show that the newly developed procedure is much more efficient than well-known methods for the numerical solution of initial value problems with oscillating solutions.

scholarly journals A Legendre Wavelet Spectral Collocation Method for Solving Oscillatory Initial Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
A. Karimi Dizicheh ◽  
F. Ismail ◽  
M. Tavassoli Kajani ◽  
Mohammad Maleki
Keyword(s):  
Differential Equation ◽  
Spectral Method ◽  
Initial Value Problems ◽  
Algebraic Equations ◽  
Initial Value ◽  
Numerical Examples ◽  
Runge Kutta Method ◽  
Collocation Points ◽  
Oscillatory Initial Value Problems ◽  
Exponentially Fitted

In this paper, we propose an iterative spectral method for solving differential equations with initial values on large intervals. In the proposed method, we first extend the Legendre wavelet suitable for large intervals, and then the Legendre-Guass collocation points of the Legendre wavelet are derived. Using this strategy, the iterative spectral method converts the differential equation to a set of algebraic equations. Solving these algebraic equations yields an approximate solution for the differential equation. The proposed method is illustrated by some numerical examples, and the result is compared with the exponentially fitted Runge-Kutta method. Our proposed method is simple and highly accurate.

DISSIPATIVE TRIGONOMETRICALLY-FITTED METHODS FOR SECOND ORDER IVPs WITH OSCILLATING SOLUTION

2002 ◽  
Vol 13 (10) ◽  
pp. 1333-1345 ◽  
Author(s):  
T. E. SIMOS
Keyword(s):  
Hybrid Method ◽  
Initial Value Problems ◽  
Oscillating Solution ◽  
Second Order ◽  
Initial Value ◽  
Step Method ◽  
Numerical Examples ◽  
Oscillating Solutions ◽  
Trigonometrical Fitting ◽  
Trigonometrically Fitted Methods

In this paper a dissipative trigonometrically-fitted two-step explicit hybrid method is developed. This method is based on a dissipative explicit two-step method developed recently by Papageorgiou, Tsitouras and Famelis.6 Numerical examples show that the procedure of trigonometrical fitting is the only way in one to produce efficient dissipative methods for the numerical solution of second order initial value problems (IVPs) with oscillating solutions.

ON THE CONSTRUCTION OF EFFICIENT METHODS FOR SECOND ORDER IVPS WITH OSCILLATING SOLUTION

2001 ◽  
Vol 12 (10) ◽  
pp. 1453-1476 ◽  
Author(s):  
T. E. SIMOS ◽  
JESUS VIGO AGUIAR
Keyword(s):  
Initial Value Problems ◽  
Multistep Methods ◽  
Oscillating Solution ◽  
Second Order ◽  
Phase Lag ◽  
Initial Value ◽  
New Methods ◽  
Oscillating Solutions ◽  
Exponentially Fitted ◽  
Minimal Phase

In this paper we describe procedures for the construction of efficient methods for the numerical solution of second order initial value problems (IVPs) with oscillating solutions. Based on the described procedures we develop two simple and efficient multistep methods for the solution of the above problems. The first method is exponentially-fitted and trigonometrically-fitted and the second has a minimal phase-lag. Both methods are symmetric. Numerical results obtained for several well known problems show the efficiency of the new methods when they are compared with known methods in the literature.

Sign in / Sign up

Export Citation Format

Share Document