A new block method with extra derivative for solving second order O.D.E

What is it about?

Block methods have been demonstrated to be the appropriate numerical methods for solving second-order ordinary differential equations. As a result, this paper describes a five-point implicit block method for addressing second-order ordinary differential equations using the third derivative. The new process was derived by interpolating Hermite polynomials. The block methods do not reduce the equation to the first-order system of ordinary differential equations; instead, they approximate the numerical solutions five points at a time. To improve the effectiveness of the suggested approach, the third derivative of the issue is included into the formula during the technique’s formulation. The accuracy of the five- point block approach is compared with many methods on approximately equal or lower orders of magnitude than that of the new process, which thus numerically interprets the accuracy and effectiveness of the new process compared to the other methods. The results showed that the new approach was superior to the others in terms of the error value, which was very small. There is a difference in the time taken to calculate the code compared to other methods.

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Photo by Anoushka Puri on Unsplash

Photo by Anoushka Puri on Unsplash

Why is it important?

The results showed that the new approach was superior to the others in terms of the error value, which was very small. There is a difference in the time taken to calculate the code compared to other methods