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Variable Step Variable Order Block Backward Differentiation Method For Solving Directly Higher Order Stiff Ordinary Differential Equations

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dc.contributor.authorAsnor, Asma Izzati
dc.date.accessioned2024-03-29T09:07:02Z
dc.date.available2024-03-29T09:07:02Z
dc.date.issued2023-09
dc.description.abstractThis thesis emphasises on developing Variable Step Variable Order Block Backward Differentiation Method (VSVO-BBDM) for solving directly higher-order stiff ordinary differential equations (ODEs). The scarcity of research on solving higher-order stiff ODEs directly, especially for order three and higher, is evident in the existing literature. As a result, it is crucial to take up the mantle of investigating and elucidating the direct solutions for these higher-order stiff ODEs, specifically for orders three and four. This method generates a set of new solutions in a block at each integration step along the interval. The first part of the thesis discusses the computational work mth-order Variable Step Block Backward Differentiation Formula (mVS-BBDF(3)) method for direct numerical solutions of third-order stiff ODEs. These problems are directly solved without going through the reduction process to the first-order system. The mVS-BBDF(3) method is implemented in the variable step size approach. Meanwhile, the second part of this thesis comprises the computational work of the VSVO-BBDM for solving the higher-order stiff ODEs directly. The computational work of the VSVO-BBDM is carried out using a strategy of varying the step size and varying the order. The advancement of this strategy is intended to enhance the efficiency of the proposed methods to approximate the solutions effectively. Besides, a detailed discussion of the convergence and stability properties of the proposed methods is also included.
dc.identifier.urihttps://erepo.usm.my/handle/123456789/18794
dc.language.isoen_US
dc.subjectVariable Step Variable
dc.subjectVariable Step Variable Order Block Backward Differentiation Method
dc.subjectSolving Directly Higher Order Stiff Ordinary Differential Equations
dc.subjectStiff Ordinary Differential Equations
dc.subjectVariable Order Block Backward
dc.subjectAsnor
dc.subjectAsma Izzati
dc.subjectAsma Izzati Binti Asnor
dc.subjectPusat Pengajian Pendidikan Jarak Jauh
dc.titleVariable Step Variable Order Block Backward Differentiation Method For Solving Directly Higher Order Stiff Ordinary Differential Equations
dc.typeResource Types::text::thesis::doctoral thesis
dspace.entity.typePublication
oairecerif.author.affiliationUniversiti Sains Malaysia
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