TY - JOUR
A2 - Andrianov, Igor
AU - Ghawadri, N.
AU - Senu, N.
AU - Ismail, F.
AU - Ibrahim, Z. B.
PY - 2018
DA - 2018/07/04
TI - Exponentially Fitted and Trigonometrically Fitted Explicit Modified Runge-Kutta Type Methods for Solving
SP - 4029371
VL - 2018
AB - Exponentially fitted and trigonometrically fitted explicit modified Runge-Kutta type (MRKT) methods for solving y′′′x=fx,y,y′ are derived in this paper. These methods are constructed which exactly integrate initial value problems whose solutions are linear combinations of the set functions eωx and e-ωx for exponentially fitted and sinωx and cosωx for trigonometrically fitted with ω∈R being the principal frequency of the problem and the frequency will be used to raise the accuracy of the methods. The new four-stage fifth-order exponentially fitted and trigonometrically fitted explicit MRKT methods are called EFMRKT5 and TFMRKT5, respectively, for solving initial value problems whose solutions involve exponential or trigonometric functions. The numerical results indicate that the new exponentially fitted and trigonometrically fitted explicit modified Runge-Kutta type methods are more efficient than existing methods in the literature.
SN - 1110-757X
UR - https://doi.org/10.1155/2018/4029371
DO - 10.1155/2018/4029371
JF - Journal of Applied Mathematics
PB - Hindawi
KW -
ER -