TEW Differential Equations and its Applications (2021)

School Convener(s)

etc. He discussed Gaussian RBF and derived the Gaussian RBF scheme for non-linear ordinary
differential equations two point boundary value problem. The second order Gauss-RBF scheme
and high order Gauss-RBF scheme were also explained. Dr. Jha delivered the material in a
friendly, fun, simple and easy way.
The Existence and uniqueness result for non-linear problems was derived. Python
algorithms for linear problem and non linear problem were discussed. He also explained fuzzy
transform method for differential equations. In this topic, Dr. Jha talked about fuzzy partition of
universe, F-transform, inverse F- transform, approximate solution of the Cauchy problem. For
the topics covered in these lectures, the plenty of examples were discussed in the tutorial.

Further he explained the stability of solution of IVP and define the well posedness of the
problem as
(i)Solution is unique
(ii)Solution continuously depends on initial data.

He also defined single and multistep methods and derived some of them with nice
explanation of Picard method, Taylor method, Euler method, Trapezoidal method and RK
methods. He made a remark that Taylor methods have the desirable property of high- order local
truncation error, but the disadvantage of requiring the computation and evaluation of the
derivatives of f (t, y). This is a complicated and time-consuming procedure for most problems, so
the Taylor methods are seldom used in practice.
Subsequently, he introduced the Runge-Kutta methods which have the high-order local
truncation error of the Taylor methods but eliminate the need to compute and evaluate the
derivatives of f(t, y). Further, he elaborated Euler and Runge-Kutta for initial value problem. In
particular, he emphasized the order of truncation for RK methods.
At the end of each lecture, speakers interacted with the audience and answered the question
raised by participants. In this way, TEW enlightened the audience about the use of concepts
explained in the workshop.
The workshop ended with formal vote of thanks by convener of the workshop Ms. Harindri
Chaudhary followed by National Anthem.