In this paper, we establish various inequalities for some differentiable mappings that are linked with the illustrious Hermite-Hadamard integral inequality for mappings whose derivatives are s-(α, m)-convex. The generalised integral inequalities contribute better estimates than some already presented. The inequalities are then applied to numerical integration and some special means.2010 Mathematics subject classification: primary 26D10; secondary 26D15, 26A51.
Differential transformation provides semi-analytical arithmetical solution. This approach is proficient at reducing calculation and works readily. In this paper, we use Elzaki transform method (ETM) and differential transformation method (DTM) to get a numerical result of the third order ordinary differential equation. We compare the results to see which method converges quickly with the true solution. We also offer numerical results with errors to show the efficiency of the methods.
We calculated Noether-like operators and first integrals of a scalar second-order ordinary differential equation using the complex Lie-symmetry method. We numerically integrated the equations using a symplectic Runge–Kutta method. It was seen that these structure-preserving numerical methods provide qualitatively correct numerical results, and good preservation of first integrals is obtained.
We calculate Noether like operators and first integrals of scalar equation y ′′ = −k 2 y using complex Lie symmetry method, by taking values of k and y to be real as well as complex. We numerically integrate the equations using a symplectic Runge-Kutta method and check for preservation of these first integrals. It is seen that these structure preserving numerical methods provide qualitatively correct numerical results and good preservation of first integrals is obtained.
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