Picard Type Iterative Scheme with Initial Iterates in Reverse Order for a Class of Nonlinear Three Point BVPs
We consider the following class of three point boundary value problem y′′(t)+f(t,y)=0, 0<t<1,y′(0)=0,y(1)=δy(η), where δ>0, 0<η<1, the source term f(t,y) is Lipschitz and continuous. We use monotone iterative technique in the presence of upper and lower solutions for both well-order a...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2013/728149 |
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| author | Mandeep Singh Amit K. Verma |
| author_facet | Mandeep Singh Amit K. Verma |
| author_sort | Mandeep Singh |
| collection | DOAJ |
| description | We consider the following class of three point boundary value problem y′′(t)+f(t,y)=0, 0<t<1,y′(0)=0,y(1)=δy(η), where δ>0, 0<η<1, the source term f(t,y) is Lipschitz and continuous. We use monotone iterative technique in the presence of upper and lower solutions for both well-order and reverse order cases. Under some sufficient conditions, we prove some new existence results. We use examples and figures to demonstrate that monotone iterative method can efficiently be used for computation of solutions of nonlinear BVPs. |
| format | Article |
| id | doaj-art-b75b743d41004deebc165b59f9dfb538 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-b75b743d41004deebc165b59f9dfb5382025-08-20T03:39:30ZengWileyInternational Journal of Differential Equations1687-96431687-96512013-01-01201310.1155/2013/728149728149Picard Type Iterative Scheme with Initial Iterates in Reverse Order for a Class of Nonlinear Three Point BVPsMandeep Singh0Amit K. Verma1Department of Mathematics, BITS Pilani, Pilani, Rajasthan 333031, IndiaDepartment of Mathematics, BITS Pilani, Pilani, Rajasthan 333031, IndiaWe consider the following class of three point boundary value problem y′′(t)+f(t,y)=0, 0<t<1,y′(0)=0,y(1)=δy(η), where δ>0, 0<η<1, the source term f(t,y) is Lipschitz and continuous. We use monotone iterative technique in the presence of upper and lower solutions for both well-order and reverse order cases. Under some sufficient conditions, we prove some new existence results. We use examples and figures to demonstrate that monotone iterative method can efficiently be used for computation of solutions of nonlinear BVPs.http://dx.doi.org/10.1155/2013/728149 |
| spellingShingle | Mandeep Singh Amit K. Verma Picard Type Iterative Scheme with Initial Iterates in Reverse Order for a Class of Nonlinear Three Point BVPs International Journal of Differential Equations |
| title | Picard Type Iterative Scheme with Initial Iterates in Reverse Order for a Class of Nonlinear Three Point BVPs |
| title_full | Picard Type Iterative Scheme with Initial Iterates in Reverse Order for a Class of Nonlinear Three Point BVPs |
| title_fullStr | Picard Type Iterative Scheme with Initial Iterates in Reverse Order for a Class of Nonlinear Three Point BVPs |
| title_full_unstemmed | Picard Type Iterative Scheme with Initial Iterates in Reverse Order for a Class of Nonlinear Three Point BVPs |
| title_short | Picard Type Iterative Scheme with Initial Iterates in Reverse Order for a Class of Nonlinear Three Point BVPs |
| title_sort | picard type iterative scheme with initial iterates in reverse order for a class of nonlinear three point bvps |
| url | http://dx.doi.org/10.1155/2013/728149 |
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