Deanship of Graduate Studies | Researches | OPTIMIZATION OF TWO-STEP HYBRID BLOCK METHOD FOR SOLVING INITIAL VALUE PROBLEMS OF THIRD ORDER ORDINARY DIFFERENTIAL EQUATIONS

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Document Details

Document Type	:	Thesis
Document Title	:	OPTIMIZATION OF TWO-STEP HYBRID BLOCK METHOD FOR SOLVING INITIAL VALUE PROBLEMS OF THIRD ORDER ORDINARY DIFFERENTIAL EQUATIONS الطريقة المثلى للكتلة الهجينة ثنائية الخطوة لحل مسائل القيمة االبتدائية للمعادالت التفاضلية العادية من الرتبة الثالثة
Subject	:	Faculty of Science
Document Language	:	Arabic
Abstract	:	Optimization of Two-Step Hybrid Block Method for Solving Initial Value Problems of Third Order Ordinary Differential Equations By Sadeem Ayed Abduallah ALqarni Supervised By Dr. Bothayna Saleh Kashkari Abstract In this thesis, The numerical solutions of Initial Value Problems of general Third Order Ordinary Differential Equations have been studied. A new class of continuous implicit Hybrid Two-step Methods has been developed using the collocation and interpolation technique of the power series approximate solution, we have selected suitable Hybrid points to optimize the local truncation errors of the main formulas. The new class of continuous implicit Hybrid Two-step Methods has the advantage of easy change of step length and evaluation of functions at two points. The Block Method used to implement the main method guarantees that each discrete method obtained from the simultaneous solution of the Block has the same order of accuracy as the main method. Hence, the new class of Two-step methods gives high order of accuracy with very low error constants, gives large intervals of absolute stability, are zero stable and converge. Sample examples of linear, nonlinear problems have been used to test the performance of the methods as well as to compare computed results and the associated errors with the exact solutions and errors of results obtained from others methods.
Supervisor	:	Dr. Bothayna Saleh Kashkari
Thesis Type	:	Master Thesis
Publishing Year	:	1441 AH 2019 AD
Added Date	:	Wednesday, December 4, 2019

Researchers

Researcher Name (Arabic)	Researcher Name (English)	Researcher Type	Dr Grade	Email
سديم عايض القرني	ALqarni, Sadeem Ayed	Researcher	Master

Files

File Name	Type	Description
45633.pdf	pdf

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