Taleb Almousa, Mohammad Salameh
(2015)
Approximate Analytical Methods For Solving Fredholm
Integral Equations.
PhD thesis, Universiti Sains Malaysia.
Abstract
Persamaan kamiran memainkan peranan penting dalam banyak bidang sains seperti
matematik, biologi, kimia, fizik, mekanik dan kejuruteraan. Oleh yang
demikian,pelbagai teknik berbeza telah digunakan untuk menyelesaikan persamaan
jenis ini. Kajian ini, memfokus kepada analisis secara matematik dan berangka bagi
beberapa kes persamaan kamiran Fredholm yang linear dan bukan linear. Kes-kes ini
termasuklah persamaan kamiran Fredholm satu dimensi jenis pertama dan kedua,
persamaan kamiran Fredholm dua dimensi jenis pertama dan kedua dan sistem
persamaan kamiran Fredholm satu dimensi dan dua dimensi.
Integral equations play an important role in many branches of sciences such as
mathematics, biology, chemistry, physics, mechanics and engineering. Therefore, many
different techniques are used to solve these types of equations. This study focuses on the
mathematical and numerical analysis of some cases of linear and nonlinear Fredholm
integral equations. These cases are one-dimensional Fredholm integral equations of the
first kind and second kind, two-dimensional Fredholm integral equations of the first kind
and second kind and systems of one and two-dimensional Fredholm integral equations.
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