## International Journal of Differential Equations

### Solving the Telegraph and Oscillatory Differential Equations by a Block Hybrid Trigonometrically Fitted Algorithm

#### Abstract

We propose a block hybrid trigonometrically fitted (BHT) method, whose coefficients are functions of the frequency and the step-size for directly solving general second-order initial value problems (IVPs), including systems arising from the semidiscretization of hyperbolic Partial Differential Equations (PDEs), such as the Telegraph equation. The BHT is formulated from eight discrete hybrid formulas which are provided by a continuous two-step hybrid trigonometrically fitted method with two off-grid points. The BHT is implemented in a block-by-block fashion; in this way, the method does not suffer from the disadvantages of requiring starting values and predictors which are inherent in predictor-corrector methods. The stability property of the BHT is discussed and the performance of the method is demonstrated on some numerical examples to show accuracy and efficiency advantages.

#### Article information

Source
Int. J. Differ. Equ., Volume 2015 (2015), Article ID 347864, 15 pages.

Dates
Received: 6 July 2015
Accepted: 22 October 2015
First available in Project Euclid: 20 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1484881453

Digital Object Identifier
doi:10.1155/2015/347864

Mathematical Reviews number (MathSciNet)
MR3431512

Zentralblatt MATH identifier
1382.65200

#### Citation

Ngwane, F. F.; Jator, S. N. Solving the Telegraph and Oscillatory Differential Equations by a Block Hybrid Trigonometrically Fitted Algorithm. Int. J. Differ. Equ. 2015 (2015), Article ID 347864, 15 pages. doi:10.1155/2015/347864. https://projecteuclid.org/euclid.ijde/1484881453

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