2000 中華民國自動控制研討會徵文啟事
... Burgers’ equation is a well-known mathematical model describing a number of physical phenomena that combine both nonlinear propagation and diffusive effects in fluid mechanics and gas dynamics. It is also related to a variety of applications such as traffic flow problems, continuous stochastic proce ...
... Burgers’ equation is a well-known mathematical model describing a number of physical phenomena that combine both nonlinear propagation and diffusive effects in fluid mechanics and gas dynamics. It is also related to a variety of applications such as traffic flow problems, continuous stochastic proce ...
preprint.
... or Ac F , where A is the stiffness matrix with entries Aij a j , i , F is the load vector with entries F j ( f , j ) , and c (c1 , c2 ,, c N ) T is the vector of unknown coefficients. Thus, having the basis functions 1 , 2 ,, N we can assemble the stiffness matrix A , the load v ...
... or Ac F , where A is the stiffness matrix with entries Aij a j , i , F is the load vector with entries F j ( f , j ) , and c (c1 , c2 ,, c N ) T is the vector of unknown coefficients. Thus, having the basis functions 1 , 2 ,, N we can assemble the stiffness matrix A , the load v ...
URL Address
... • The above algorithms are intended to solve nonstiff systems. If they appear to be unduly slow, try using one of the stiff solvers below. • ode15s is a variable order solver based on the numerical differentiation formulas (NDFs). Optionally, it uses the backward differentiation formulas (BDFs, also ...
... • The above algorithms are intended to solve nonstiff systems. If they appear to be unduly slow, try using one of the stiff solvers below. • ode15s is a variable order solver based on the numerical differentiation formulas (NDFs). Optionally, it uses the backward differentiation formulas (BDFs, also ...
1 (3 hrs.)
... (c) Suppose, instead of solving the problem analytically, the set of ODE-IVP is to be integrated using Crank-Nicholson method (i.e. trapezoidal rule). Find the condition on the integration step size ’h’in terms of eigenvalues of matrix A so that the approximation error will decay exponentially and ...
... (c) Suppose, instead of solving the problem analytically, the set of ODE-IVP is to be integrated using Crank-Nicholson method (i.e. trapezoidal rule). Find the condition on the integration step size ’h’in terms of eigenvalues of matrix A so that the approximation error will decay exponentially and ...
IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728.
... From above comparison table we have shown that Milne’s (modified) predictor-corrector formulae gives better accuracy and it also can minimize the calculating time as it takes less number of iterations. But, it is yet to implement proposed formulae to the real world problems. Though Milne’s (modified ...
... From above comparison table we have shown that Milne’s (modified) predictor-corrector formulae gives better accuracy and it also can minimize the calculating time as it takes less number of iterations. But, it is yet to implement proposed formulae to the real world problems. Though Milne’s (modified ...
HOW TO FIGHT THE WRAPPING EFFECT Karl Nickel Institut fUr
... X(t) is "known" when G(t) is "given". Since X is always nonsingular the known function h defines an also known function k. Hence the two forms (5) and (9) of a linear system are both equivalent theoretically and from a computational point of view. There are even real life problems which lead to line ...
... X(t) is "known" when G(t) is "given". Since X is always nonsingular the known function h defines an also known function k. Hence the two forms (5) and (9) of a linear system are both equivalent theoretically and from a computational point of view. There are even real life problems which lead to line ...
8th Tutorial - Mathematics and Statistics
... (IVP). Here we will focus on obtaining approximations for y at various values, called mesh points or time steps, in the interval [a, b], instead of obtaining a continuous approximation to the solution y. Once we know the approximation solution at the mesh points, we can use interpolation to get an a ...
... (IVP). Here we will focus on obtaining approximations for y at various values, called mesh points or time steps, in the interval [a, b], instead of obtaining a continuous approximation to the solution y. Once we know the approximation solution at the mesh points, we can use interpolation to get an a ...
Numerical Analysis PhD Qualifying Exam University of Vermont, Spring 2010
... University of Vermont, Spring 2010 1. This question concerns number representation and errors. Normalized floating point numbers can be represented by ±1.b1 b2 b3 . . . bN × 2±p where bi is either 0 or 1, N is the number of bits in the mantissa, p is an M -bit binary exponent, and two additional bit ...
... University of Vermont, Spring 2010 1. This question concerns number representation and errors. Normalized floating point numbers can be represented by ±1.b1 b2 b3 . . . bN × 2±p where bi is either 0 or 1, N is the number of bits in the mantissa, p is an M -bit binary exponent, and two additional bit ...
1.4 Notes
... Section 1.4: The Approximation Method of Euler There are three general approaches to solving DE’s. The analytic approach will be the major focus of the course. We were introduced to a graphical approach in Section 1.3, where we got information about solutions by sketching direction fields. In this s ...
... Section 1.4: The Approximation Method of Euler There are three general approaches to solving DE’s. The analytic approach will be the major focus of the course. We were introduced to a graphical approach in Section 1.3, where we got information about solutions by sketching direction fields. In this s ...
Numerical Approximation of Forward
... constant coefficients α, β and γ, they have considered the problem of finding a differentiable solution on a certain real interval [−1, k], given its values at the intervals [−1, 0] and (k − 1, k]. They have concluded that in general the specification of such boundary functions is not sufficient to ...
... constant coefficients α, β and γ, they have considered the problem of finding a differentiable solution on a certain real interval [−1, k], given its values at the intervals [−1, 0] and (k − 1, k]. They have concluded that in general the specification of such boundary functions is not sufficient to ...
4yx = + 2 xy = ⌋ ⌉ ⌊ ⌈ = xy 11 J ⌋ ⌉ ⌊ ⌈ -
... The standard normal distribution value was obtained from appendix A.3 of WMM. (b) What PDF did you use to solve part (a)? I would use the normal distribution because the molecular weight can be considered to be a continuous variable. Moreover, we only know the mean and the variance, so we have enoug ...
... The standard normal distribution value was obtained from appendix A.3 of WMM. (b) What PDF did you use to solve part (a)? I would use the normal distribution because the molecular weight can be considered to be a continuous variable. Moreover, we only know the mean and the variance, so we have enoug ...
Notes_Chapter_1
... • If these isoclines are simple and familiar curves, we first sketch several of them, then draw short line segments with the same slope c at representative points of each isocline f(x, y) = c. ...
... • If these isoclines are simple and familiar curves, we first sketch several of them, then draw short line segments with the same slope c at representative points of each isocline f(x, y) = c. ...
Solving a Cubic Equation by Perturbation Theory
... You probably do not know how to solve the equation x3 + ...
... You probably do not know how to solve the equation x3 + ...
NARESUAN UNIVERSITY FACULTY OF ENGINEERING The Finite
... a wide range of the physical problems that may be characterized by energy theorems, functionals or differential equations with a prescribed set of boundary conditions. These problems may be as diversed as structural, elasticity, heat transfer, fluid flow, magnetic field, soil-structure interaction, ...
... a wide range of the physical problems that may be characterized by energy theorems, functionals or differential equations with a prescribed set of boundary conditions. These problems may be as diversed as structural, elasticity, heat transfer, fluid flow, magnetic field, soil-structure interaction, ...
Solution
... It thus only remains in each of the three cases to find a second test function, giving a second equation for the two unknowns. a. ...
... It thus only remains in each of the three cases to find a second test function, giving a second equation for the two unknowns. a. ...
MATH10232: SOLUTION SHEET I
... where the MATLAB notation x(1:100) means “select the first 100 entries in the array x”. The result is 0.01, which is also the case if we take the right-hand end of each interval to be the x values. The fact that the error seems to be equal to the size of the interval if we assume that we are approxi ...
... where the MATLAB notation x(1:100) means “select the first 100 entries in the array x”. The result is 0.01, which is also the case if we take the right-hand end of each interval to be the x values. The fact that the error seems to be equal to the size of the interval if we assume that we are approxi ...
Here
... 2. Show that the finite difference discretization of (x + 1)uxx + (y2 + 1)uyy - u = 1 0 x 1, 0 y 1, x = y = 1/3 with u(0,y) = y, u(1,y) = y2, u(x,0) = 0, u(x,1) = 1 is given by ...
... 2. Show that the finite difference discretization of (x + 1)uxx + (y2 + 1)uyy - u = 1 0 x 1, 0 y 1, x = y = 1/3 with u(0,y) = y, u(1,y) = y2, u(x,0) = 0, u(x,1) = 1 is given by ...
Interval finite element
The interval finite element method (interval FEM) is a finite element method that uses interval parameters. Interval FEM can be applied in situations where it is not possible to get reliable probabilistic characteristics of the structure. This is important in concrete structures, wood structures, geomechanics, composite structures, biomechanics and in many other areas [1]. The goal of the Interval Finite Element is to find upper and lower bounds of different characteristics of the model (e.g. stress, displacements, yield surface etc.) and use these results in the design process. This is so called worst case design, which is closely related to the limit state design. Worst case design require less information than probabilistic design however the results are more conservative [Köylüoglu and Elishakoff 1998].