HAAR WAVELETS & SOLUTIONS OF BVPs WITH APPLICATIONS TO LINGUISTIC HIERARCHIES

Under the mentorship of Prof. Shiraz Minwalla, Breakthrough Prize (New Horizons) Prize Winner

S.T. Yau High School Science Award (Asia) - Finalist (Math)

ABSTRACT

In this report, various problems regarding differential equations are studied when ordinary differential equations (ODEs) have a complicated solution by a direct method. When this type of problem arises, we always try to use the numerical solution method but, we have solved it by using Haar wavelets.

Before coming directly to the solution, we have studied the Haar wavelets. Then we have discussed the properties of Haar wavelets. Then we have discussed the advantages of the application of Haar wavelets in an ordinary differential equation in short, and other applications of wavelets in ODEs and examples based on boundary value problems (BVPs).

In addition to mathematical problems, the concept of Haar wavelets can also be extended to model linguistic signals, such as speech or sound, which behave as non-stationary time-dependent systems. The same mathematical framework used to represent boundary value problems can be applied to analyze how linguistic signals vary across time, capturing both local and global changes in pitch, intensity, and structure.