-
Convergence Analysis for Wave Equation by Explicit Finite Difference Equation with Drichlet and Neumann Boundary Condition
Issue:
Volume 7, Issue 2, June 2021
Pages:
19-24
Received:
24 October 2020
Accepted:
3 May 2021
Published:
26 May 2021
Abstract: There are many problems in the field of science, engineering and technology which can be solved by differential equations formulation. The wave equation is a second order linear hyperbolic partial differential equation that describes the propagation of variety of waves, such as sound or water waves. In this paper we consider the convergence analysis of the explicit schemes for solving one dimensional, time-dependent wave equation with Drichlet and Neumann boundary condition. Taylor's series expansion is used to expand the finite difference approximations in the explicit scheme. We present the derivation of the schemes and develop a computer program to implement it We use spectral radius of Matrix obtained from discretization and Von Neumann stability condition to determine stability, and consistence of the method from truncated error from discretized method. Using Lax Equivalence Theorem, convergence of the methods was described by testing consistency and stability of the methods. And it is found out that the scheme is stable with the Drichlet boundary and conditionally stable with Derivative boundary condition.
Abstract: There are many problems in the field of science, engineering and technology which can be solved by differential equations formulation. The wave equation is a second order linear hyperbolic partial differential equation that describes the propagation of variety of waves, such as sound or water waves. In this paper we consider the convergence analysi...
Show More
-
Some New Properties of Wd-fuzzy Implication Algebras
Issue:
Volume 7, Issue 2, June 2021
Pages:
25-29
Received:
23 April 2021
Accepted:
4 May 2021
Published:
27 May 2021
Abstract: Implication is an important logical connective in practically every propositional logic. In 1987, the so-called Fuzzy implication algebras were introduced by Wu Wangming, then various interesting properties of FI-algebras and some subalgebra of Fuzzy implication algebra, such as regular FI-algebras, commutative FI-algebras, Wd- FI-algebras, and other kinds of FI- algebras were reported. The main aim of this article is to study Wd-fuzzy implication algebras which are subalgebra of fuzzy implication algebras. We showed that Wd-fuzzy implication algebras are regular fuzzy implication algebras, but the inverse is not true. The relations between Wd-fuzzy implication algebras and other fuzzy algebras are discussed. Properties and axiomatic systems for Wd-fuzzy implication algebras are investigated. Furthermore, a few new results on Wd-fuzzy implication algebras has been added.
Abstract: Implication is an important logical connective in practically every propositional logic. In 1987, the so-called Fuzzy implication algebras were introduced by Wu Wangming, then various interesting properties of FI-algebras and some subalgebra of Fuzzy implication algebra, such as regular FI-algebras, commutative FI-algebras, Wd- FI-algebras, and oth...
Show More
-
A Study of Operators on Fuzzy Sets
Alhaji Jibril Alkali,
Sylvanus Kupongoh Samaila
Issue:
Volume 7, Issue 2, June 2021
Pages:
30-36
Received:
4 April 2021
Accepted:
20 May 2021
Published:
15 June 2021
Abstract: Overtime, mathematics had been used as a tool in modeling real life phenomenon. In some cases, these problems cannot fit-into the classical deterministic or stochastic modeling techniques, perhaps due system complexity arising from lack of complete knowledge about the phenomenon or some uncertainty. The uncertainty could either be due to lack of clear boundaries in the description of the object or perhaps due to randomness. In this article, we study a mathematical tool discovered in 1965 by Zadeh suitable for modeling real life phenomenon and examined operations on such a tool. Motivated by the work of Zadeh, we studied operators on Type-1 Fuzzy Sets (T1FSs) and Type-2 Fuzzy sets (T2FSs) and provided examples, one of which is a variant of the Yager complement function for which the complement operator was graphically illustrated. The joint and the meet operators were also studied and examples provided. Non-standard operators were defined on T1FSs and T2FSs and also classified into two groups; the triangular-norm (t-norm) and triangular-conorm (t-conorm). Using t-norm and t-conorm, an example was adopted from Castillo and Aguilar to illustrate the computation of the standard operation on T2FSs. Finally, future research direction was provided based on what is yet to be achieved in fuzzy set theory.
Abstract: Overtime, mathematics had been used as a tool in modeling real life phenomenon. In some cases, these problems cannot fit-into the classical deterministic or stochastic modeling techniques, perhaps due system complexity arising from lack of complete knowledge about the phenomenon or some uncertainty. The uncertainty could either be due to lack of cl...
Show More
