Download or read book An Implicit Numerical Method for Solving the Two dimensional Heat Equation written by George A. Baker and published by . This book was released on 1958 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Comparison of Implicit Numerical Methods for Solving the Transient Spherical Diffusion Equation written by and published by . This book was released on 1977 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Oscillatory Solutions of the Peaceman Rachford Alternating Direction Implicit Method and a Comparison of Methods for the Solution of the Two Dimensional Heat Diffusion Equation written by R. F. Kropf and published by . This book was released on 1985 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two dimensional heat diffusion equation with Dirichlet boundary conditions was solved using the fully explicit, fully implicit, Crank-Nicolson implicit, and Peaceman-Rachford alternating direction implicit (ADI) methods. Comparisons of accuracy and time requirements were made. The possibility that the ADI method has stable oscillatory solutions with large time steps was investigated. Results of computations revealed that the ADI has stable oscillations for large time steps, in some cases producing large enough errors to render the solution unusable. Time steps greater than twice the square of the mesh spacing divided by the thermal diffusivity must be used with care. For small time steps, the Crank-Nicolson and ADI methods were the most accurate, and the ADI was the fastest method. The fully implicit method was the most accurate at large time steps, but the ADI, with a smaller time step to reduce the oscillatory error, was still the fastest method to reach a solution with the desired degree of accuracy. Additional keywords: theses; numerical analysis; finite difference theory; conduction (heat transfer); partial differential equations; stability.(Author).
Download or read book Solving Two dimensional Heat Equation Using Alternating Direction Implicit Method written by Nur Ain Ayunni Sabri and published by . This book was released on 2009 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Numerical Analysis written by Curtis F. Gerald and published by Addison Wesley Publishing Company. This book was released on 1984 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Difference Methods in Heat Transfer written by M. Necati Özişik and published by CRC Press. This book was released on 2017-07-12 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Difference Methods in Heat Transfer presents a clear, step-by-step delineation of finite difference methods for solving engineering problems governed by ordinary and partial differential equations, with emphasis on heat transfer applications. The finite difference techniques presented apply to the numerical solution of problems governed by similar differential equations encountered in many other fields. Fundamental concepts are introduced in an easy-to-follow manner. Representative examples illustrate the application of a variety of powerful and widely used finite difference techniques. The physical situations considered include the steady state and transient heat conduction, phase-change involving melting and solidification, steady and transient forced convection inside ducts, free convection over a flat plate, hyperbolic heat conduction, nonlinear diffusion, numerical grid generation techniques, and hybrid numerical-analytic solutions.
Download or read book The One Dimensional Heat Equation written by John Rozier Cannon and published by Cambridge University Press. This book was released on 1984-12-28 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a version of Gevrey's classical treatise on the heat equations. Included in this volume are discussions of initial and/or boundary value problems, numerical methods, free boundary problems and parameter determination problems. The material is presented as a monograph and/or information source book. After the first six chapters of standard classical material, each chapter is written as a self-contained unit except for an occasional reference to elementary definitions, theorems and lemmas in previous chapters.
Download or read book Solution of Two dimensional Heat Problems Using the Alternating Direction Method written by Frederick James Leipold and published by . This book was released on 1967 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite difference approximations to the one-dimensional heat equation Ut = Uxx are used to introduce explicit and implicit difference equations. The convergence and stability of these equations is discussed and those concepts are used to show the restrictions imposed on explicit equations. The Implicit Alternating Direction (IAD) method is introduced as a means for solution of the two-dimensional heat equation. Although the IAD method in its basic form is applicable only to parabolic problems it is possible by slight modification to apply the method to elliptic problems. Two examples are used to illustrate the use of the IAD method for solution of parabolic and elliptic equations for a rectangular region. These examples include a work requirement comparision with other difference methods. A third example is given to show the applicability of the IAD method to non-rectangular regions, in this case a parabolic problem over a circular region. Results of these examples show that the IAD method is a convenient and accurate method when applied to both parabolic and elliptic partial differential equations and suggest applicability to a wide range of problems. (Author).
Download or read book Numerical Methods for Solving Linear Systems and Applications to Elliptic Difference Equations written by Clarence Edgar Lee and published by . This book was released on 1959 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iterative numerical methods for solving independent, simultaneous, inhomogeneous linear equations are surveyed. Application of the methods to elliptic difference equations as arise in neutron diffasion, heat conduction, and potential problems is discussed.
Download or read book Introduction To Numerical Computation An Second Edition written by Wen Shen and published by World Scientific. This book was released on 2019-08-28 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as a set of lecture notes for a senior undergraduate level course on the introduction to numerical computation, which was developed through 4 semesters of teaching the course over 10 years. The book requires minimum background knowledge from the students, including only a three-semester of calculus, and a bit on matrices.The book covers many of the introductory topics for a first course in numerical computation, which fits in the short time frame of a semester course. Topics range from polynomial approximations and interpolation, to numerical methods for ODEs and PDEs. Emphasis was made more on algorithm development, basic mathematical ideas behind the algorithms, and the implementation in Matlab.The book is supplemented by two sets of videos, available through the author's YouTube channel. Homework problem sets are provided for each chapter, and complete answer sets are available for instructors upon request.The second edition contains a set of selected advanced topics, written in a self-contained manner, suitable for self-learning or as additional material for an honored version of the course. Videos are also available for these added topics.
Download or read book Application of the Hughes Liu Algorithm to the Two dimensional Heat Equation written by David S. Malkus and published by . This book was released on 1982 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Solution of Two dimensional Heat Problems Using the Alternating Direction Method written by and published by . This book was released on 1967 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite difference approximations to the one-dimensional heat equation Ut = Uxx are used to introduce explicit and implicit difference equations. The convergence and stability of these equations is discussed and those concepts are used to show the restrictions imposed on explicit equations. The Implicit Alternating Direction (IAD) method is introduced as a means for solution of the two-dimensional heat equation. Although the IAD method in its basic form is applicable only to parabolic problems it is possible by slight modification to apply the method to elliptic problems. Two examples are used to illustrate the use of the IAD method for solution of parabolic and elliptic equations for a rectangular region. These examples include a work requirement comparision with other difference methods. A third example is given to show the applicability of the IAD method to non-rectangular regions, in this case a parabolic problem over a circular region. Results of these examples show that the IAD method is a convenient and accurate method when applied to both parabolic and elliptic partial differential equations and suggest applicability to a wide range of problems. (Author).
Download or read book NASA Technical Translation written by and published by . This book was released on 1976 with total page 912 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Numerical Methods Using MATLAB written by Won Y. Yang and published by John Wiley & Sons. This book was released on 2005-05-20 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, with the introduction of new media products, there has been a shift in the use of programming languages from FORTRAN or C to MATLAB for implementing numerical methods. This book makes use of the powerful MATLAB software to avoid complex derivations, and to teach the fundamental concepts using the software to solve practical problems. Over the years, many textbooks have been written on the subject of numerical methods. Based on their course experience, the authors use a more practical approach and link every method to real engineering and/or science problems. The main benefit is that engineers don't have to know the mathematical theory in order to apply the numerical methods for solving their real-life problems. An Instructor's Manual presenting detailed solutions to all the problems in the book is available online.
Download or read book Application of the Hughes LIU Algorithm to the 2 dimensional Heat Equation written by and published by . This book was released on 1982 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Programming for Computations Python written by Svein Linge and published by Springer. This book was released on 2016-07-25 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.
Download or read book Numerical Methods in Heat Transfer written by Kenneth E. Torrance and published by . This book was released on 1985 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
