Abstract
The EDITRK5 method. which this paper derives. is an exponentially fitted diagonally implicit RK method for solving ODEs with the equation With the help of the set functions and for exponentially fitting problems. this strategy is designed to integrate precise initial value problems (IVPs). The primary frequency of the issue. is used to increase the method's accuracy. The new approach For the purpose of solving IVPs using exponential functions as solutions. EDITRK5 is a novel three-stage five-order exponentially-fitted diagonally implicit method. When the same issue is reduced to the first-order framework of equations. which can be solved using traditional RK approaches. different forms of third-order ODEs must be constructed using the new system. and numerical comparisons must be made. The numerical results demonstrate that the new strategy is more effective than methods that have already been published.
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