scholarly journals Eksistensi dan Ketunggalan Solusi Persamaan Diferensial Linier Advance-Delay Homogen

2019 ◽  
Vol 4 (4) ◽  
pp. 153
Author(s):  
Devi Silvia Rahimi
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Initial Value ◽  
Method Of Steps

Pada tulisan ini akan dikonstruksi solusi persamaan diferensial linier advancedelay homogen. Selanjutnya, dengan menggunakan metode langkah (method of steps) dapat ditunjukkan bahwa suatu fungsi awal dengan syarat tertentu menjamin eksistensi dan ketunggalan solusinya. Tulisan ini mengeksplorasi kembali studi yang dilakukan oleh Ford dan Lumb (J. Compt. App. Math. 229, 2007).Kata Kunci: Differential Equations, Initial Value Problem, heaviside

On Nagumo's Condition

1972 ◽  
Vol 15 (4) ◽  
pp. 609-611 ◽  
Author(s):  
Thomas Rogers
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Uniqueness Theorem ◽  
Initial Value Problem ◽  
Initial Value ◽  
Image Position

The classical uniqueness theorem of Nagumo [1] for ordinary differential equations is as follows.Theorem. If f(t, y) is continuous on 0≤t≤1, -∞<y<∞ and ifthen there is at most one solution to the initial value problem y'=f(t, y), y(0)=0.

A Parallel Block Predictor-Corrector Method by Python-Based Distributed Computing

2012 ◽  
Vol 263-266 ◽  
pp. 1315-1318
Author(s):  
Kun Ming Yu ◽  
Ming Gong Lee
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Numerical Method ◽  
Initial Value Problem ◽  
Message Passing ◽  
Message Passing Interface ◽  
Parallel Structure ◽  
Initial Value ◽  
Speed Up ◽  
Predictor Corrector

This paper is to discuss how Python can be used in designing a cluster parallel computation environment in numerical solution of some block predictor-corrector method for ordinary differential equations. In the parallel process, MPI-2(message passing interface) is used as a standard of MPICH2 to communicate between CPUs. The operation of data receiving and sending are operated and controlled by mpi4py which is based on Python. Implementation of a block predictor-corrector numerical method with one and two CPUs respectively is used to test the performance of some initial value problem. Minor speed up is obtained due to small size problems and few CPUs used in the scheme, though the establishment of this scheme by Python is valuable due to very few research has been carried in this kind of parallel structure under Python.

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