Existence and Uniqueness Analysis for a Class of Singular Non-Linear Two-Point Boundary Value Problems by an Optimal Iterative Sequence
محورهای موضوعی : مجله بین المللی ریاضیات صنعتی
E. Shivanian
1
(
Department of Mathematics, Imam Khomeini International
University, Qazvin, Iran.
)
کلید واژه: Singular boundary value problem, Constructive theorem, Existence and uniqueness, Convergence,
چکیده مقاله :
The convergence of thisiterative sequence is then controlled by an embedded parameter. The fastest convergence occurs for an optimal embedded parameter which maximizes a special function. This optimization problem brings a sequence with high rate of the convergence to theunique solution in the finite region where $\frac{\partial f}{\partial y}$ has to be positive.Some illustrative examples are given to confirm the validity and reliability of this constructive theory.
در این مقاله، یک اثبات ساختاری برای مطالعه وجود و منحصر به فرد بودن جواب مساله منفرد زیر با شرایط مرزی ارائه می شود. به طور کلی فرض می شود که نسبت متغیر مستقل نامنفرد باشد. اما مجاز است نسبت به منفرد باشد. دنباله تکراری پیکارد را با ساخت معادله انتگرالی که تابع گرین در آن منفی نیست، اعمال می کنیم. سپس همگرایی این دنباله تکراری توسط یک پارامتر نشانده کنترل می شود. سریعترین همگرایی برای یک پارامتر نشانده بهینه رخ می دهد که یک تابع خاص را به حداکثر می رساند. این مسئله بهینه‌سازی دنباله‌ای با سرعت بالایی از همگرایی به جواب یکتا به ارمغان می‌آورد بطوریکه در ناحیه محدود به آن باید مثبت باشد. چند مثال گویا برای تایید اعتبار و پایایی این بحث ساختلری آورده شده است.
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