Current Issue : January - March Volume : 2016 Issue Number : 1 Articles : 5 Articles
ThispapermainlypresentsEulermethodandfourthorderRungeKuttaMethod(RK4)forsolving\ninitialvalueproblems(IVP)forordinarydifferentialequations(ODE).Thetwoproposedmethods\narequiteefficientandpracticallywellsuitedforsolvingtheseproblems.Inordertoverifytheac\ncuracy,wecomparenumericalsolutionswiththeexactsolutions.Thenumericalsolutionsarein\ngood agreement with the exact solutions. Numerical comparisons between Euler method and\nRungeKuttamethodhavebeenpresented.Alsowecomparetheperformanceandthecomputa\ntional effort of suchmethods. In order to achieve higher accuracy in the solution, the step size\nneedstobeverysmall.Finallyweinvestigateandcomputetheerrorsofthetwoproposedmeth\nodsfordifferentstepsizestoexaminesuperiority.Severalnumericalexamplesaregiventodem\nonstratethereliabilityandefficiency....
The finite difference method such as alternating group iterative methods is useful in numerical\nmethod for evolutionary equations and this is the standard approach taken in this paper. Alternating\ngroup explicit (AGE) iterative methods for one-dimensional convection diffusion equations\nproblems are given. The stability and convergence are analyzed by the linear method. Numerical\nresults of the model problem are taken. Known test problems have been studied to demonstrate\nthe accuracy of the method. Numerical results show that the behavior of the method with emphasis\non treatment of boundary conditions is valuable....
The phenomenon of extinction is an important property of solutions for many evolutionary equations.\nIn this paper, a numerical simulation for computing the extinction time of nonnegative solutions\nfor some nonlinear parabolic equations on general domains is presented. The solution algorithm\nutilizes the Donor-cell scheme in space and Euler�s method in time. Finally, we will give\nsome numerical experiments to illustrate our algorithm....
First, the effectivity of classical Proper Generalized Decomposition (PGD) computational\nmethods is analyzed on a one dimensional transient diffusion benchmark problem,\nwith a moving load. Classical PGD methods refer to Galerkin, Petrovââ?¬â??Galerkin and Minimum\nResidual formulations. A new and promising PGD computational method based\non the Constitutive Relation Error concept is then proposed and provides an improved,\nimmediate and robust reduction error estimation. All those methods are compared to\na reference Singular Value Decomposition reduced solution using the energy norm.\nEventually, the variable separation assumption itself (here time and space) is analyzed\nwith respect to the loading velocity....
In this article, a technique is proposed for obtaining better and accurate results for\nnonlinear PDEs. We constructed abundant exact solutions via exp(âË?â??Ãâ?¢(Ã?·))-expansion\nmethod for the Zakharovââ?¬â??Kuznetsov-modified equal-width (ZK-MEW) equation and\nthe (2 + 1)-dimensional Burgers equation. The traveling wave solutions are found\nthrough the hyperbolic functions, the trigonometric functions and the rational functions.\nThe specified idea is very pragmatic for PDEs, and could be extended to engineering\nproblems....
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