Project ID: 216
MUHAMMAD SHAHIERUL EIZMAN BIN MOHD SHUHAINI - CS247
2016284344
Supervisor: MOHD RIVAIE BIN MOHD ALI (DR)
Examiner: MOHD RIVAIE BIN MOHD ALI (DR)
SOLVING ORDINARY DIFFERENTIAL EQUATION USING LEAST SQUARE METHOD: APPLICATION OF THE CONJUGATE GRADIENT METHOD
Abstract
For solving order nonhomogeneous Ordinary differential equation with boundary value
theorem (BVP) is important. Because it is commonly appear in range of field and
profession such as engineering and physics. There are two theoretical methods used to
solve this problem which are undetermined coefficient and variation of parameter.
Besides, this theoretical method is really complicated to understood and it will take a
long time to solve the problems. Other researchers likely to use numerical method in
the form of least square method. The difficulty by using the two theoretical methods
which is undermined coefficient and variations of parameter is high compared to
numerical method. End of the least square method that will be use, Conjugate Gradient
is used to solve the inverse matrix to avoid ill-conditioned matrix. The error will be
analysed based on the solution of both exact and approximate methods. Numerical
solution will show that Least Square Method can solved second-order nonhomogeneous
ordinary differential equation with BVP based on term of the error analysis made by
theoretical method which are undetermined coefficient and variation of parameter and
numerical method.