توسیع ضمنی روش سری تیلور با مشتقات عددی برای حل مسائل مقدار اولیه
Parallel Title Proper
Implicit Extension of Taylor Series Method with Numerical Derivatives for Initial Value Problems
First Statement of Responsibility
/زانیار حمدی
.PUBLICATION, DISTRIBUTION, ETC
Name of Publisher, Distributor, etc.
: علوم ریاضی
Date of Publication, Distribution, etc.
، ۱۳۹۷
Name of Manufacturer
، راشدی
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
۶۰ص
NOTES PERTAINING TO PUBLICATION, DISTRIBUTION, ETC.
Text of Note
چاپی - الکترونیکی
DISSERTATION (THESIS) NOTE
Dissertation or thesis details and type of degree
کارشناسی ارشد
Discipline of degree
ریاضی کاربردی گرایش آنالیز عددی
Date of degree
۱۳۹۸/۰۸/۱۹
Body granting the degree
تبریز
SUMMARY OR ABSTRACT
Text of Note
روش سری تیلور از جمله اولین روشهای عددی حل مسایل مقدار اولیه است .در این پایاننامه، روش سری تیلور با تقریب مشتقات بالا با تکنیهای تفاضل متناه بهبود میابد .چند الوریتم سری تیلور صریح با مشتق عددی و توسیع ضمن آنها معرف شده و خواص سازگاری و پایداری الوریتمها بررس مشوند .الوریتمهای معرف شده مجهز به تکنی طول گام متغیر خواهند بود .کارایی روشهای معرف شده با ارایه چند مثال عددی نشان داده مشود
Text of Note
The Taylor series method is one of the earliest analytic-numeric algorithms for approximate solution of initial value problems for ordinary differential equations. The main idea of the rehabilitation of this algorithms is based on the approximate calculation of higher derivatives using well-known finite-difference technique for the partial differential equations. The approximate solution is given as a piecewise polynomial function defined on the subintervals of the whole interval integration. This property offers different facility for adaptive error control. This dissertation describes several explicit Taylor series algorithms with numerical derivatives and their implicit extension and examines its consistency and stability properties. The implicit extension based on a collocation term added to the explicit truncated Taylor series and the approximate solution obtained as a continuously differentiable piecewise polynomials function. Some numerical test results is presented to prove the efficiency of these new-old algorithm
PARALLEL TITLE PROPER
Parallel Title
Implicit Extension of Taylor Series Method with Numerical Derivatives for Initial Value Problems