Solving Initial Value Problems with Mendeleev’s Quadrature
Abstract
This article presents the Mendeleev method to solve the initial value problems. The construction of this method using Mendeleev’s
quadrature by Pleshakov [Comp. Math. and Math. Phys., 52 (2012),
211-212.] to approximate the integral
R xi+1
xi
f(Y (s))ds. We derive the local truncation error and show the stability region of the proposed method. The computational comparisons show that Mendeleev’s
method is better than Euler’s method, midpoint method and Heun’s
method.
quadrature by Pleshakov [Comp. Math. and Math. Phys., 52 (2012),
211-212.] to approximate the integral
R xi+1
xi
f(Y (s))ds. We derive the local truncation error and show the stability region of the proposed method. The computational comparisons show that Mendeleev’s
method is better than Euler’s method, midpoint method and Heun’s
method.
Keywords
Initial value problems, Mendeleev’s quadra- ture, Euler’s method, midpoint method, Heun’s method, stability region.
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