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Galerkin Method for Numerical Solution of Volterra Integro-Differential Equations with Certain Orthogonal Basis Function

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International Journal of Modern Nonlinear Theory and Application 2023年第2期12卷 68-80页

作者： Omotayo Adebayo Taiwo Liman Kibokun Alhassan olutunde samuel odetunde Olatayo Olusegun Alabi Department of Mathematics University of Ilorin Ilorin Nigeria Department of Mathematical Sciences Olabisi Onabanjo University Ago-Iwoye Nigeria Department of Statistics Federal University of Technology Akure Nigeria

This paper concerns the implementation of the orthogonal polynomials using the Galerkin method for solving Volterra integro-differential and Fredholm integro-differential equations. The constructed orthogonal polynomials are used as basis functions in the assumed solution employed. Numerical examples for some selected problems are provided and the results obtained show that the Galerkin method with orthogonal polynomials as basis functions performed creditably well in terms of absolute errors obtained.

关键词： Galerkin Method Integro-Differential Equation Orthogonal Polynomials Basis Function Approximate Solution

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Galerkin Method for Numerical Solution of Volterra Integro-Differential Equations with Certain Orthogonal Basis Function

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International Journal of Modern Nonlinear Theory and Application（现代非线性理论与应用） 2023年第2期

作者： Omotayo Adebayo Taiwo Liman Kibokun Alhassan olutunde samuel odetunde Olatayo Olusegun Alabi

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Phylogenetics and Molecular Divergence of Tilapia Fish (Oreochromis Species) Using Mitochondrial D-Loop and Cytochrome b Regions

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American Journal of Molecular Biology 2018年第1期8卷 39-57页

作者： Ekerette Emmanuel Ekerette Ekei Victor Ikpeme Ogbuagu Ugorji Udensi Michael Ohiokhuaobo Ozoje Owoidihe Monday Etukudo Anthony John Umoyen samuel olutunde Durosaro Matthew Wheto Department of Genetics and Biotechnology University of Calabar Calabar Nigeria Department of Animal Breeding and Genetics Federal University of Agriculture Abeokuta Nigeria

Understanding the level of genetic diversity in any population is an important requisite towards strategizing measures for conservation and improvement of stocks. This study focused on the assessment of phylogenetics and molecular divergence of tilapia fish species obtained from two populations (Domita in South-South and Odeda in South-West, Nigeria) using the displacement loop (D-loop) and cytochrome b region of the mitochondrial deoxyribonucleic acid (mtDNA). A total of 28 samples (15 from South-South and 13 from South-West) were used for the genetic analysis. DNA was extracted from the tissue of all the samples using Quik-gDNATM miniPrep kit. The D-loop containing the hypervariable region was sequenced for all samples from the two populations, while cytochrome b (Cyt b) region of mtDNA was only sequenced for samples from South-South population. Chromatograms of the sequences were viewed and edited using Bioedit software. Multiple sequence alignment was carried out using molecular evolutionary genetic analysis (MEGA) software before subsequent genetic analyses. Phylogenetic analysis grouped the samples into two clusters based on population. Also, when the two mitochondrial regions were pooled together, they clustered into two major groups based on mitochondrial regions. Analysis of molecular variance (AMOVA) revealed 37.32% variation within population and 62.68% variation among population with a significant fixation index of 0.627 (p 0.05). The genetic distance inferred between D-loop regions of South-South and South-West populations was 0.243. Maternal lineage analysis revealed that the origin of tilapia fish from both populations could be traced to Oreochromis spirilus and Oreochromis leucostictus based on mitochondrial D-loop region. The findings of this study revealed molecular divergence among the tilapia populations and may serve as pivot information for the genetic improvement of this important species.

关键词： Phylogenetics Molecular Divergence Maternal Lineage Tilapia Fish

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