a comparative evaluation of matlab, octave, freemat - here

... limited to the basic functionalities of Matlab itself; Matlab does have a very rich set of toolboxes for a large variety of applications or for certain areas with more sophisticated algorithms. If the use of one of them is profitable or integral to the research, the other packages are likely not via ...

... limited to the basic functionalities of Matlab itself; Matlab does have a very rich set of toolboxes for a large variety of applications or for certain areas with more sophisticated algorithms. If the use of one of them is profitable or integral to the research, the other packages are likely not via ...

A Review of Recent Developments in Solving ODES

... will decay very quickly and, for all practical purposes, may become zero. For components that are insignificant, we are usually interested only in their size, and do not need to compute them accurately. Suppose that we use an explicit method like Euler’s method to solve such a problem, where, for ex ...

... will decay very quickly and, for all practical purposes, may become zero. For components that are insignificant, we are usually interested only in their size, and do not need to compute them accurately. Suppose that we use an explicit method like Euler’s method to solve such a problem, where, for ex ...

Iterative Methods for Systems of Equations

... the presence of a train. A voltage is applied to the rails at one end of a section of track and a relay is attached across the other end, so that the relay is energised if no train is present, whereas the wheels of a train will short circuit the relay, causing it to de-energise. Any failure in the p ...

... the presence of a train. A voltage is applied to the rails at one end of a section of track and a relay is attached across the other end, so that the relay is energised if no train is present, whereas the wheels of a train will short circuit the relay, causing it to de-energise. Any failure in the p ...

Numerical Solution of Fuzzy Polynomials by Newton

... quantities are presented in parametric form. We first convert the polynomial fuzzy coefficients into parametric form then apply Newton method on each limit. Finally, in order to finding root, which is also fuzzy number/point, we numerically calculate level sets (i.e., -cuts) of fuzzy coefficients ...

... quantities are presented in parametric form. We first convert the polynomial fuzzy coefficients into parametric form then apply Newton method on each limit. Finally, in order to finding root, which is also fuzzy number/point, we numerically calculate level sets (i.e., -cuts) of fuzzy coefficients ...

Numerical Solution of Differential Equations with Orthogonal

... Thus the derivative at any collocation point can be determined in terms of the solution at the collocation points. Once we know the solution at all collocation points we can find d. And once we know d we can find the solution for any x. If we wish to find the solution at a point that is not ...

... Thus the derivative at any collocation point can be determined in terms of the solution at the collocation points. Once we know the solution at all collocation points we can find d. And once we know d we can find the solution for any x. If we wish to find the solution at a point that is not ...

Adomian Method for Second-order Fuzzy Differential Equation

... differential equation” was introduced in 1987 by Kandel and Byatt [21,22]. There have been many suggestions for the deﬁnition of fuzzy derivative to study FDE. The ﬁrst and the most popular approach is using the Hukuhara differentiability for fuzzy-value functions. Under this setting, mainly the exi ...

... differential equation” was introduced in 1987 by Kandel and Byatt [21,22]. There have been many suggestions for the deﬁnition of fuzzy derivative to study FDE. The ﬁrst and the most popular approach is using the Hukuhara differentiability for fuzzy-value functions. Under this setting, mainly the exi ...

ENGR-25_Lec-21_Linear_Equations-2

... OVERdetermined systems cont. – For overdetermined systems that have no exact solution, the estimated-answer given by the left-division method satisfies the equation set only in a LEAST SQUARES sense – When we use MATLAB to solve an overdetermined set, the program does not tell us whether the solutio ...

... OVERdetermined systems cont. – For overdetermined systems that have no exact solution, the estimated-answer given by the left-division method satisfies the equation set only in a LEAST SQUARES sense – When we use MATLAB to solve an overdetermined set, the program does not tell us whether the solutio ...

a new approach to solve fuzzy non-linear equations using fixed

... In algebra, it is easy to solve literal equations ( ) = 0 of all degrees up to and including fourth. But we are not always able to get exact solution of equations. Besides this, no general method exists for finding the roots of this equation in terms of their co-efficient. It is always possible to c ...

... In algebra, it is easy to solve literal equations ( ) = 0 of all degrees up to and including fourth. But we are not always able to get exact solution of equations. Besides this, no general method exists for finding the roots of this equation in terms of their co-efficient. It is always possible to c ...

Introduction to Initial Value Problems

... at more and more points (which much be chosen in a uniform manner) then its solution will approach the exact solution to the IVP. The simplest methods for approximating the solution to our prototype IVP are the forward and backward Euler methods which we derive by approximating the derivative in the ...

... at more and more points (which much be chosen in a uniform manner) then its solution will approach the exact solution to the IVP. The simplest methods for approximating the solution to our prototype IVP are the forward and backward Euler methods which we derive by approximating the derivative in the ...

A virtual element method with arbitrary regularity

... us to design a family of numerical methods that are associated with discrete spaces with arbitrary C α regularity and are suitable for general unstructured polygonal meshes. To this end, we propose a new VEM that depends on two integer parameters: α for the regularity and m for the polynomial degree ...

... us to design a family of numerical methods that are associated with discrete spaces with arbitrary C α regularity and are suitable for general unstructured polygonal meshes. To this end, we propose a new VEM that depends on two integer parameters: α for the regularity and m for the polynomial degree ...

Numerical Methods for the solution of Hyperbolic

... The mathematical description of many practical problems in science and engineering leads to conservation laws, that is time-dependent systems of partial differential equations (PDEs), usually hyperbolic and nonlinear, with a particularly simple structure. Fluid and gas dynamics, relativity theory, q ...

... The mathematical description of many practical problems in science and engineering leads to conservation laws, that is time-dependent systems of partial differential equations (PDEs), usually hyperbolic and nonlinear, with a particularly simple structure. Fluid and gas dynamics, relativity theory, q ...

Numerical Methods for Partial Differential Equations

... • However, it is also reasonable to ask if we can solve it approximately. • We have now simplified as far as possible. • Once we can solve this model problem numerically, we will apply this technique using the method of lines to approximate the solution of the PDE. CAAM 452 Spring 2005 ...

... • However, it is also reasonable to ask if we can solve it approximately. • We have now simplified as far as possible. • Once we can solve this model problem numerically, we will apply this technique using the method of lines to approximate the solution of the PDE. CAAM 452 Spring 2005 ...

Free vibration of annular and circular plates of stepped thickness

... problem can be obtained by using the Green’s function method. This method in the previous papers [3-6] was used, but the problems there considered concern the axisymmetric free vibrations of annular or circular uniform plates with elastic ring supports. The present paper deals with free vibrations o ...

... problem can be obtained by using the Green’s function method. This method in the previous papers [3-6] was used, but the problems there considered concern the axisymmetric free vibrations of annular or circular uniform plates with elastic ring supports. The present paper deals with free vibrations o ...

PDF (Chapter 1 - Initial-Value Problems for

... From (1.19) one can explain the oscillations in the solution for N = 10 and 20. If (1 + hA) < 0 then the numerical solution will alternate in sign. For (1 + hA) to be equal to zero, hA = -1. When N = 10 or 20, hA is less than -1 and therefore oscillations in the solution occur. For this problem, it ...

... From (1.19) one can explain the oscillations in the solution for N = 10 and 20. If (1 + hA) < 0 then the numerical solution will alternate in sign. For (1 + hA) to be equal to zero, hA = -1. When N = 10 or 20, hA is less than -1 and therefore oscillations in the solution occur. For this problem, it ...

PDF

... Cervical spine injuries occur as a result of impact or from large inertial forces such as those experienced by military pilots during ejections, carrier landings, and ditchings. Other examples include motor vehicle, diving, and athletic related accidents. Reducing the likelihood of injury by identif ...

... Cervical spine injuries occur as a result of impact or from large inertial forces such as those experienced by military pilots during ejections, carrier landings, and ditchings. Other examples include motor vehicle, diving, and athletic related accidents. Reducing the likelihood of injury by identif ...

Abstract summaries - ICCM International Committee on

... Interaction of Matrix Cracking and Delamination in Cross-Ply Laminates: Simulations with Stochastic Cohesive Zone Elements VV Silberschmidt, ZR Khokhar, IA Ashcroft (Loughborough Univ) This paper is aimed at the interaction between matrix cracking and delamination failure mechanisms in CFRP cross-pl ...

... Interaction of Matrix Cracking and Delamination in Cross-Ply Laminates: Simulations with Stochastic Cohesive Zone Elements VV Silberschmidt, ZR Khokhar, IA Ashcroft (Loughborough Univ) This paper is aimed at the interaction between matrix cracking and delamination failure mechanisms in CFRP cross-pl ...

PDF

... variables. Rather than use these inputs directly, the deterministic FE code may alternatively require cross-sectional properties such as area and moments of inertia to be defined. To handle this and similar situations, NESSUS provides a Fortran subroutine for defining FE input quantities in terms of ...

... variables. Rather than use these inputs directly, the deterministic FE code may alternatively require cross-sectional properties such as area and moments of inertia to be defined. To handle this and similar situations, NESSUS provides a Fortran subroutine for defining FE input quantities in terms of ...

An Analytic Approximation to the Solution of

... loss accuracy in the results. Analytical methods commonly used for solving Schrodinger equation are very restricted and can be used in very special cases so they can not be used to solve equations of numerous realistic scenarios. The variational iteration method which is a modified general Lagrange ...

... loss accuracy in the results. Analytical methods commonly used for solving Schrodinger equation are very restricted and can be used in very special cases so they can not be used to solve equations of numerous realistic scenarios. The variational iteration method which is a modified general Lagrange ...

A Greens Function Numerical Method for Solving Parabolic Partial

... This proof lays the foundation for an important result which we will offer as a proposition, but will not prove here. Indeed, it can be shown that the previous result can be extended to arbitrarily many spacial dimensions. Proposition 2.5. The Green function for the heat equation with zero Dirichlet ...

... This proof lays the foundation for an important result which we will offer as a proposition, but will not prove here. Indeed, it can be shown that the previous result can be extended to arbitrarily many spacial dimensions. Proposition 2.5. The Green function for the heat equation with zero Dirichlet ...

1.10 Euler`s Method

... differential equation. Rather they generate a sequence of approximations to the value of the solution at speciﬁed points. Furthermore, if we use a sufﬁcient number of points, then by plotting the points (xi , yi ) and joining them with straight-line segments, we are able to obtain an overall approxi ...

... differential equation. Rather they generate a sequence of approximations to the value of the solution at speciﬁed points. Furthermore, if we use a sufﬁcient number of points, then by plotting the points (xi , yi ) and joining them with straight-line segments, we are able to obtain an overall approxi ...

A class of Methods Based on Cubic Non

... Since , 1 3,1 , 3,1 3,0 ,and 3, 0 are positive. Using inequalities (26) and (31), we obtain ...

... Since , 1 3,1 , 3,1 3,0 ,and 3, 0 are positive. Using inequalities (26) and (31), we obtain ...

Chapter 8: Nonlinear Equations

... Numerical Root-Finding using Newton or Secan t Method: FindRoot[ f(x)==expr, {x, x0}] - Newton’s Method using starting value x0. FindRoot[ f(x)==expr, {x, x0, xmin, xmax}] - use starting value x0; stop if x goes outside range xmin to xmax. FindRoot[ {eqn1, eqn2, . . . }, {x, x0}, {y, y0}, . . . ] - ...

... Numerical Root-Finding using Newton or Secan t Method: FindRoot[ f(x)==expr, {x, x0}] - Newton’s Method using starting value x0. FindRoot[ f(x)==expr, {x, x0, xmin, xmax}] - use starting value x0; stop if x goes outside range xmin to xmax. FindRoot[ {eqn1, eqn2, . . . }, {x, x0}, {y, y0}, . . . ] - ...

Numerical solution of nonlinear system of parial differential

... Here we will investigate the construction of the Pade approximates[10] for the functions studied. The main advantage of Pade approximation over the Taylor series approximation is that the Taylor series approximation can exhibit oscillati which may produce an approximation error bound. Moreover, Tayl ...

... Here we will investigate the construction of the Pade approximates[10] for the functions studied. The main advantage of Pade approximation over the Taylor series approximation is that the Taylor series approximation can exhibit oscillati which may produce an approximation error bound. Moreover, Tayl ...

Iso-P2 P1/P1/P1 Domain-Decomposition/Finite

... the Reynolds number is set to 400. The boundary condition and the external force are calculated from the stationary Navier-Stokes equations. We have divided Ω into a union of uniform N ×N ×2 triangular elements, where N = 4, 8, 16 or 32. We have computed in two domain-decomposed ways, where the numb ...

... the Reynolds number is set to 400. The boundary condition and the external force are calculated from the stationary Navier-Stokes equations. We have divided Ω into a union of uniform N ×N ×2 triangular elements, where N = 4, 8, 16 or 32. We have computed in two domain-decomposed ways, where the numb ...

# 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].