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Numerical Analysis and Computation Commons™
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Full-Text Articles in Numerical Analysis and Computation
Iterative Methods To Solve Systems Of Nonlinear Algebraic Equations, Md Shafiful Alam
Iterative Methods To Solve Systems Of Nonlinear Algebraic Equations, Md Shafiful Alam
Masters Theses & Specialist Projects
Iterative methods have been a very important area of study in numerical analysis since the inception of computational science. Their use ranges from solving algebraic equations to systems of differential equations and many more. In this thesis, we discuss several iterative methods, however our main focus is Newton's method. We present a detailed study of Newton's method, its order of convergence and the asymptotic error constant when solving problems of various types as well as analyze several pitfalls, which can affect convergence. We also pose some necessary and sufficient conditions on the function f for higher order of convergence. Different …
Nabla Fractional Calculus And Its Application In Analyzing Tumor Growth Of Cancer, Fang Wu
Nabla Fractional Calculus And Its Application In Analyzing Tumor Growth Of Cancer, Fang Wu
Masters Theses & Specialist Projects
This thesis consists of six chapters. In the first chapter, we review some basic definitions and concepts of fractional calculus. Then we introduce fractional difference equations involving the Riemann-Liouville operator of real number order between zero and one. In the second chapter, we apply the Brouwer fixed point and Contraction Mapping Theorems to prove that there exists a solution for up to the first order nabla fractional difference equation with an initial condition. In chapter three, we define a lower and an upper solution for up to the first order nabla fractional difference equation with an initial condition. Under certain …
An Algorithm To Generate Two-Dimensional Drawings Of Conway Algebraic Knots, Jen-Fu Tung
An Algorithm To Generate Two-Dimensional Drawings Of Conway Algebraic Knots, Jen-Fu Tung
Masters Theses & Specialist Projects
The problem of finding an efficient algorithm to create a two-dimensional embedding of a knot diagram is not an easy one. Typically, knots with a large number of crossings will not nicely generate two-dimensional drawings. This thesis presents an efficient algorithm to generate a knot and to create a nice two-dimensional embedding of the knot. For the purpose of this thesis a drawing is “nice” if the number of tangles in the diagram consisting of half-twists is minimal. More specifically, the algorithm generates prime, alternating Conway algebraic knots in O(n) time where n is the number of crossings …
Fractional Calculus: Definitions And Applications, Joseph M. Kimeu
Fractional Calculus: Definitions And Applications, Joseph M. Kimeu
Masters Theses & Specialist Projects
No abstract provided.