Abstract:
A differential equation along with a set of additional constraints (called boundary
conditions) form a boundary value problem. Boundary value problems (linear or
nonlinear) are found mostly in engineering, applied mathematics and physical sciences
as well. Although, few numerical algorithms are found in solving the higher
order boundary value problems using orthogonal polynomials. Since polynomials
play a vital role in computing the numerical solutions of the differential equations
therefore, the research, conducted during my PhD programme, concerns with the
study of the numerical solutions of higher order linear boundary value problems. The
main objectives of the research are to develop Galerkin technique for solving special
eighth, tenth and twelfth order linear boundary value problems using Legendre
polynomials, and numerical approximations for solving the system of Fredholm
integro–differential equations and the system of differential equations using
Laguerre polynomials. The numerical schemes, developed, have been compared with
the existing methods, which shows the higher accuracy of the schemes.
