Approximation of Solution of Some m-Point Boundary Value Problems on Time Scales
The method of upper and lower solutions and the generalized quasilinearization technique for second-order nonlinear m-point dynamic equations on time scales of the type xΔΔ(t)=f(t,xσ), t∈[0,1]T=[0,1]∩T, x(0)=0, x(σ2(1))=�...
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| Format: | Article |
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SpringerOpen
2010-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://dx.doi.org/10.1155/2010/841643 |
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doaj-806299a3a5a94d89bafc68e7cae37cae2020-11-25T00:45:01ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472010-01-01201010.1155/2010/841643Approximation of Solution of Some m-Point Boundary Value Problems on Time ScalesRahmat Ali KhanMohammad RafiqueThe method of upper and lower solutions and the generalized quasilinearization technique for second-order nonlinear m-point dynamic equations on time scales of the type xΔΔ(t)=f(t,xσ), t∈[0,1]T=[0,1]∩T, x(0)=0, x(σ2(1))=∑i=1m-1αix(ηi), ηi∈(0,1)T, ∑i=1m-1αi≤1, are developed. A monotone sequence of solutions of linear problems converging uniformly and quadratically to a solution of the problem is obtained. http://dx.doi.org/10.1155/2010/841643 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Rahmat Ali Khan Mohammad Rafique |
| spellingShingle |
Rahmat Ali Khan Mohammad Rafique Approximation of Solution of Some m-Point Boundary Value Problems on Time Scales Advances in Difference Equations |
| author_facet |
Rahmat Ali Khan Mohammad Rafique |
| author_sort |
Rahmat Ali Khan |
| title |
Approximation of Solution of Some m-Point Boundary Value Problems on Time Scales |
| title_short |
Approximation of Solution of Some m-Point Boundary Value Problems on Time Scales |
| title_full |
Approximation of Solution of Some m-Point Boundary Value Problems on Time Scales |
| title_fullStr |
Approximation of Solution of Some m-Point Boundary Value Problems on Time Scales |
| title_full_unstemmed |
Approximation of Solution of Some m-Point Boundary Value Problems on Time Scales |
| title_sort |
approximation of solution of some m-point boundary value problems on time scales |
| publisher |
SpringerOpen |
| series |
Advances in Difference Equations |
| issn |
1687-1839 1687-1847 |
| publishDate |
2010-01-01 |
| description |
The method of upper and lower solutions and the generalized quasilinearization technique for second-order nonlinear m-point dynamic equations on time scales of the type xΔΔ(t)=f(t,xσ), t∈[0,1]T=[0,1]∩T, x(0)=0, x(σ2(1))=∑i=1m-1αix(ηi), ηi∈(0,1)T, ∑i=1m-1αi≤1, are developed. A monotone sequence of solutions of linear problems converging uniformly and quadratically to a solution of the problem is obtained. |
| url |
http://dx.doi.org/10.1155/2010/841643 |
| work_keys_str_mv |
AT rahmatalikhan approximationofsolutionofsomempointboundaryvalueproblemsontimescales AT mohammadrafique approximationofsolutionofsomempointboundaryvalueproblemsontimescales |
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1725271808736755712 |