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 yx=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 ωR 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 -