• Dr. Kaushila Nandan Srivastava

This paper is concerned with the problem of developing numerical inte- gration algorithms for differential equations that, when viewed as equations in some Euclidean space, naturally evolve on some embedded submanifold. It is desired to con- struct algorithms whose iterates also evolve on the same manifold. These algorithms can therefore be viewed as integrating ordinary differential equations on manifolds. The basic method "decouples" the computation of flows on the submanifold from the numerical integration process. It is shown that two classes of single-step and multistep algorithms can be posed and analyzed theoretically, using the concept of "freezing" the coefficients of differential operators obtained from the defining vector field. Ex- plicit third-order algorithms are derived, with additional equations augmenting those of their classical counterparts, obtained from "obstructions" defined by nonvanishing Lie brackets.

numerical integration, manifold, differential equation flow, lie algebra, algorithm, symbolic computation, frozen coefficients.

"Numerical Integration of Differential Equations on Manifolds", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 1, page no.997-1000, January-2019, Available :http://www.jetir.org/papers/JETIR1901C35.pdf

"Numerical Integration of Differential Equations on Manifolds", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 1, page no. pp997-1000, January-2019, Available at : http://www.jetir.org/papers/JETIR1901C35.pdf