A-stable optimal hybrid linear multistep formulas in Runge-Kutta form and their application to dynamical systems
Keywords:
Convergence analysis, Order, Local Truncation error, Wavelet Newton approach, Chebyshev,, Block methodAbstract
A-stable optimal hybrid Linear Multistep Formulas (LMFs) are developed and reformulated as RungeKutta-type schemes because of their excellent properties in handling the numerical solution of stiff differential
equations. The LMFs are obtained using collocation and interpolation techniques and are reformulated as
Runge-Kutta-type schemes via Butcher tableau. The resulting methods, when analyzed, have algebraic order
six, and the A-stability characteristics of the proposed schemes are established. Newton’s algorithm was
adopted to handle the implicit nature of the suggested methods. The reformulated schemes are applied to
Lorenz, Chau, Rossler, and Chen systems and four other standard stiff problems in the cited literature. A
comparative study between the new method and the Dormand Prince scheme, popularly called ode45 in
Matrix Laboratory (MatLab), is presented. The experiments demonstrate the latest methods’ performance,
indicating their potential for high accuracy and competitiveness with other established codes.
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