FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W156637204> ?p ?o ?g. }

• W156637204 abstract "In this thesis, an efficient algorithm and a code BVPDI is developed forsolving Boundary Value Problems (BVPs) for Ordinary Differential Equations(ODEs). A generalised variable order variable stepsize Direct Integration (01)method, a generalised Backward Differentiation method (BDF) and shootingtechniques are used to solve the given BVP. When using simple shootingtechnique, sometimes stability difficulties arise when the differential operator ofthe given ODE contains rapidly growing and decaying fundamental solutionmodes. Then the initial value solution is very sensitive to small changes in theinitial condition. In order to decrease the bound of this error, the size of domainsover which the Initial Value Problems (IVPs) are integrated has to be restricted.This leads to the multiple shooting technique, which is generalisation of thesimple shooting technique. Multiple shooting technique for higher order ODEswith automatic partitioning is designed and successfully implemented in thecode BVPDI, to solve the underlying IVP. The well conditioning of a higher order BVP is shown to be related tobounding quantities, one involving the boundary conditions and the otherinvolving the Green's function. It is also shown that the conditioning of themultiple shooting matrix is related to the given BVP. The numerical results arethen compared with the only existing direct method code COLNEW. Theadvantages in computational time and the accuracy of the computed solution,especially, when the range of interval is large, are pointed out. Also theadvantages of BVPDI are clearer when the results are compared with the NAGsubroutine D02SAF (reduction method).Stiffness tests for the system of first order ODEs and the techniques ofidentifying the equations causing stiffness in a system a rediscussed. Theanalysis is extended for the higher order ODEs. Numerical results are discussedindicating the advantages of BVPDI code over COLNEW.The success of the BVP DI code applied to the general class of BVPs isthe motivation to con sider the same code for a special class of second orderBVPs called Sturm-Liouville (SL) problems. By the application of Floquet theoryand shooting algorithm, eigenvalues of SL problems with periodic boundaryconditions are determined without reducing to the first order system ofequations. Some numerical examples are given to illustrate the success of themethod. The results are then compared, when the same problem is reduced tothe first order system of equations and the advantages are indicated. The codeBVPDI developed in this thesis clearly demonstrates the efficiency of using DIMethod and shooting techniques for solving higher order BVP for ODEs." @default.
• W156637204 created "2016-06-24" @default.
• W156637204 creator A5053547987 @default.
• W156637204 date "1999-10-01" @default.
• W156637204 modified "2023-09-27" @default.
• W156637204 title "Solving Boundary Value Problems for Ordinary DifferentialEquations Using Direct Integration and Shooting Techniques" @default.
• W156637204 hasPublicationYear "1999" @default.
• W156637204 type Work @default.
• W156637204 sameAs 156637204 @default.
• W156637204 citedByCount "0" @default.
• W156637204 crossrefType "dissertation" @default.
• W156637204 hasAuthorship W156637204A5053547987 @default.
• W156637204 hasConcept C104317684 @default.
• W156637204 hasConcept C111335779 @default.
• W156637204 hasConcept C112972136 @default.
• W156637204 hasConcept C119857082 @default.
• W156637204 hasConcept C126255220 @default.
• W156637204 hasConcept C134306372 @default.
• W156637204 hasConcept C158448853 @default.
• W156637204 hasConcept C159985019 @default.
• W156637204 hasConcept C17020691 @default.
• W156637204 hasConcept C177264268 @default.
• W156637204 hasConcept C182310444 @default.
• W156637204 hasConcept C182365436 @default.
• W156637204 hasConcept C185592680 @default.
• W156637204 hasConcept C192562407 @default.
• W156637204 hasConcept C199360897 @default.
• W156637204 hasConcept C204323151 @default.
• W156637204 hasConcept C2524010 @default.
• W156637204 hasConcept C26955809 @default.
• W156637204 hasConcept C2776760102 @default.
• W156637204 hasConcept C28826006 @default.
• W156637204 hasConcept C33923547 @default.
• W156637204 hasConcept C34862557 @default.
• W156637204 hasConcept C41008148 @default.
• W156637204 hasConcept C4195266 @default.
• W156637204 hasConcept C51544822 @default.
• W156637204 hasConcept C55493867 @default.
• W156637204 hasConcept C78045399 @default.
• W156637204 hasConcept C86339819 @default.
• W156637204 hasConceptScore W156637204C104317684 @default.
• W156637204 hasConceptScore W156637204C111335779 @default.
• W156637204 hasConceptScore W156637204C112972136 @default.
• W156637204 hasConceptScore W156637204C119857082 @default.
• W156637204 hasConceptScore W156637204C126255220 @default.
• W156637204 hasConceptScore W156637204C134306372 @default.
• W156637204 hasConceptScore W156637204C158448853 @default.
• W156637204 hasConceptScore W156637204C159985019 @default.
• W156637204 hasConceptScore W156637204C17020691 @default.
• W156637204 hasConceptScore W156637204C177264268 @default.
• W156637204 hasConceptScore W156637204C182310444 @default.
• W156637204 hasConceptScore W156637204C182365436 @default.
• W156637204 hasConceptScore W156637204C185592680 @default.
• W156637204 hasConceptScore W156637204C192562407 @default.
• W156637204 hasConceptScore W156637204C199360897 @default.
• W156637204 hasConceptScore W156637204C204323151 @default.
• W156637204 hasConceptScore W156637204C2524010 @default.
• W156637204 hasConceptScore W156637204C26955809 @default.
• W156637204 hasConceptScore W156637204C2776760102 @default.
• W156637204 hasConceptScore W156637204C28826006 @default.
• W156637204 hasConceptScore W156637204C33923547 @default.
• W156637204 hasConceptScore W156637204C34862557 @default.
• W156637204 hasConceptScore W156637204C41008148 @default.
• W156637204 hasConceptScore W156637204C4195266 @default.
• W156637204 hasConceptScore W156637204C51544822 @default.
• W156637204 hasConceptScore W156637204C55493867 @default.
• W156637204 hasConceptScore W156637204C78045399 @default.
• W156637204 hasConceptScore W156637204C86339819 @default.
• W156637204 hasLocation W1566372041 @default.
• W156637204 hasOpenAccess W156637204 @default.
• W156637204 hasPrimaryLocation W1566372041 @default.
• W156637204 hasRelatedWork W127391941 @default.
• W156637204 hasRelatedWork W1597956837 @default.
• W156637204 hasRelatedWork W1972061314 @default.
• W156637204 hasRelatedWork W2069809965 @default.
• W156637204 hasRelatedWork W2117432795 @default.
• W156637204 hasRelatedWork W2188598241 @default.
• W156637204 hasRelatedWork W2189173066 @default.
• W156637204 hasRelatedWork W2371275697 @default.
• W156637204 hasRelatedWork W2505315915 @default.
• W156637204 hasRelatedWork W2587696763 @default.
• W156637204 hasRelatedWork W2766845580 @default.
• W156637204 hasRelatedWork W2798523373 @default.
• W156637204 hasRelatedWork W2895115404 @default.
• W156637204 hasRelatedWork W2952818876 @default.
• W156637204 hasRelatedWork W3035475691 @default.
• W156637204 hasRelatedWork W3090942923 @default.
• W156637204 hasRelatedWork W97931617 @default.
• W156637204 hasRelatedWork W2182505865 @default.
• W156637204 hasRelatedWork W2188421951 @default.
• W156637204 hasRelatedWork W2967909205 @default.
• W156637204 isParatext "false" @default.
• W156637204 isRetracted "false" @default.
• W156637204 magId "156637204" @default.
• W156637204 workType "dissertation" @default.