Numerical solution of initial value problems based on the double exponential transformation

Trigonometrically fitted two-step obrechkoff methods for the numerical solution of periodic initial value problems

In this paper, we present a new two-step trigonometrically fitted symmetric Obrechkoff method. The method is based on the symmetric two-step Obrechkoff method, with eighth algebraic order, high phase-lag order and is constructed to solve IVPs with periodic solutions such as orbital problems. We compare the new method to some recently constructed optimized methods from the literature. The numeri...

Numerical solution of fuzzy initial value problems under generalized dierentiability by HPM

Numerical Solution of Nonlinear Fin Problems via Initial Value Method

In general the mathematical model for steady, one-dimensional conduction in fins appears as a nonlinear, two-point boundaryvalue problem. The nonlinearities arise due to radiative surface heat transfer, temperature dependent thermal conductivity or heat transfer coefficient etc. [i]. Often in such cases a numerical solution has to be obtained. Examining the literature reporting such solutions i...

The symmetric two-step P-stable nonlinear predictor-corrector‎ ‎methods for the numerical solution of second order‎ ‎initial value problems

In this paper‎, ‎we propose a modification of the second order method‎ ‎introduced in [‎‎Q. Li and ‎X‎. ‎Y. ‎Wu‎, A two-step explicit $P$-stable method for solving second order initial value problems‎, ‎textit{‎Appl‎. ‎Math‎. ‎Comput‎.}‎ {‎138}‎ (2003)‎, no. 2-3, ‎435--442‎] for the numerical solution of‎ ‎IVPs for second order ODEs‎. ‎The numerical results obtained by the‎ ‎new method for some...

Implicit One-step L-stable Generalized Hybrid Methods for the Numerical Solution of First Order Initial Value problems

In this paper, we introduce the new class of implicit L-stable generalized hybrid methods for the numerical solution of first order initial value problems. We generalize the hybrid methods with utilize ynv directly in the right hand side of classical hybrid methods. The numerical experimentation showed that our method is considerably more efficient compared to well known methods used for the n...