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Texas A&M University
Mathematics

AMUSE

Date: September 12, 2018

Time: 6:00PM - 7:00PM

Location: BLOC 220

Speaker: Jay Standridge, Undergraduate Student, Department of Aerospace Engineering, TAMU

  

Title: Approximating the solutions to differential equations using orthogonal polynomials

Abstract: The topic of differential equations is an ever growing one. However, as in many mathematical problems, numerical methods are extremely useful, if not necessary. In this talk, we will explore the use numerical methods to solve differential equations, how two polynomials can be considered orthogonal, and how we can use a set of orthogonal polynomials to approximate the solution to differential equations, as well as the efficacy and limits of doing so. In short, one is able to solve an arbitrary linear differential operator with appropriate initial and/or boundary values to 6-16 decimal places depending on the difficulty of the problem and how many polynomials are used in the solution.