Diagonally Implicit Runge-Kutta Methods for Solving Linear ODEs ab 58.99 € als Taschenbuch: Numerical Methods for ODEs. Aus dem Bereich: Bücher, Wissenschaft, Mathematik,
The book deals with the basic concepts of fluid dynamics and heat, mass transfer behavior of Newtonian and non-Newtonian fluid past an extending surfaces. The considered subject is perceived by the researchers and post-doctoral researchers. In this book we introduces computational numerical tool for solving highly non-linear differential equations models that arise in flow of fluid, heat and mass transfer of both Newtonian/non-Newtonian fluid problem. Self similar solutions are obtained using the fourth-fifth order Runge-Kutta-Fehlberg method. The considered work has great importance in the field of science and technology. The considered problem is quite useful in guided missiles, rain erosion, uidization, atmospheric fallout, paint and aerosol spraying,lunar ash ows,and cooling of nuclear reactor.
This book deals with the elementary aspects of flow, heat and mass transfer of boundary layer flow problems related to magneto hydrodynamic non- Newtonian nanofluid flows , with special emphasis on slip flow and melting heat transfer so that the subject is perceived by the post graduate students, researchers and post-doctoral researchers. This text also introduces numerical computational tools for solving differential equation models that arise in fluid flow, heat and mass- transfer of non-Newtonian fluids. This study is essentially numerical in character. By applying the similarity transformations, the system of non-linear partial differential equations are reduced into a set of non-linear ordinary differential equations. Obtained equations are then solved numerically using Runge-Kutta-Fehlberg-45 order method along with Shooting technique.
The study of flow-induced noise, known as aeroacoustics, is concerned with the sound generated by turbulent and/or unsteady vortical flows including the effects of any solid boundaries in the flow. Flow-induced noise is a serious problem in many engineering applications. The most notorious one is the jet noise. In this work a shock-capturing adaptive filter is designed. It is indispensable with non linear propagation of acoustic waves or in cases when discontinuities are presents. With the combination of Dispersion Relation Schemes, Runge-Kutta optimized algorithm, selective and nonlinear filter it is possible to calculate directly acoustic and aerodynamic field in a single computation, by solving the compressible unsteady Navier-Stokes equations. Actually, traditional theories using acoustic analogy are appropriate for predicting noise when a sufficiently accurate solution of turbulent flow is available. On the contrary, the approach proposed here can be applied to cases when aerodynamic sources are influenced by acoustic motion such as flames, jet or wake instabilities. This work has been done in collaboration with Dr. Christophe Bogey of École Centrale de Lyon, France.
This book studies the numerical analysis of the system of six coupled nonlinear Ordinary Differential Equations (ODEs) which are aroused in the reduction of stratified Boussinesq Equation. This book aims to introduce the several methods of solving coupled differential equations, which occur rather frequently in the study of stratified Boussinesq equations. This book also includes the unique ways of solving coupled ODEs by Modified Euler Method, Runge-Kutta fourth order method and Adomian Decomposition Method which was originally introduced the author by himself.
This book deals with the derivation of diagonally implicit Runge-Kutta (DIRK) methods of order four and five which are specially designed for the integration of linear ordinary differential equations (LODEs). The restriction to LODEs with constant coefficients reduces the number of order equations which the coefficients of Runge-Kutta (RK) methods must satisfy. The coefficients of the RK methods are chosen such that the error norm is minimized, this resulted in methods which are almost one order higher than the actual order. The stability polynomials and stability regions of the methods are then obtained using MATHEMATICA package. Codes using C++ programming based on the methods are developed to test sets of problems on linear ordinary differential equations. Numerical results show that the new methods are more efficient than the existing methods.
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics and computational science, Heun''s method (also called the modified Euler''s method or the explicit trapezoidal rule), named after Karl L. W. M. Heun, is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It can be seen as an extension of the Euler method into a two-stage second-order Runge Kutta method.
In numerical analysis, the Dormand Prince method is a method for solving ordinary differential equations (Dormand & Prince 1980). The method is a member of the Runge Kutta family of ODE solvers. More specifically, it uses six function evaluations to calculate fourth- and fifth-order accurate solutions. The difference between these solutions is then taken to be the error of the (fourth-order) solution. This error estimate is very convenient for adaptive stepsize integration algorithms. Other similar integration methods are Fehlberg (RKF) and Cash Karp (RKCK).
This book contains the elementary aspects of flow, heat and mass transfer of boundary layer flow problems related to Oldroyd-B fluid and Casson fluid with suspended nano particles, with special emphasis on slip flow and nonlinear thermal radiation so that the subject is perceived by the post graduate students, researchers and post-doctoral researchers. This text is also introduces numerical computational tools for solving differential equation models that arises in fluid flow, heat and mass transfer of non-Newtonian fluids. Suitable similarity transformations are applied to the governing partial differential equations to obtain coupled nonlinear ordinary differential equations. The reduced equations are solved numerically by using Runge-Kutta-Fehlberg fourth-fifth order method with Shooting technique.