NEWLY GENERATED ORTHOGONAL BESSEL POLYNOMIAL TO SOLVE FINITE BOUNDARY VALUE PROBLEMS, AND INFINITE BOUNDARY VALUE MHD CASSON FLUID FLOWING ACROSS A STRETCHED SHEET
Prithvi S., Patil Mallikarjun B.
Department of Studies and Research in Mathematics, Tumkur University, Jnanasiri Campus, Bidarakatte, Tumakuru, Karnataka – – 572 118, India
Abstract: This article introduces a newly developed Orthogonal Bessel Polynomial and employs the operational matrix of integration approach for solving problems with finite and infinite boundary conditions. In this method, we utilise the Bessel polynomial operational matrix collocation technique to convert the differential equations into a system of nonlinear algebraic equations at various collocating points. These resulting algebraic equations are then solved to obtain the solution to the differential equations. To validate the method, we tested it on multiple problems and observed that the results demonstrated excellent convergence and agreement. For solving differential equations with infinite boundary conditions, we considered the flow of MHD Casson fluid over a permeable stretching sheet, solved the governing equations, and analysed the resulting graphs, providing insights into the behaviour of the system. It could be observed from the calculations below that orthogonal Bessel polynomials provide better results when compared to the non-orthogonal Bessel polynomials.
Keywords: Bessel Polynomial, Orthogonal, Weight Function, Casson Fluid, Stretching Sheet.
VOLUME 9 ISSUE 12 2025: 81 – 101