meshfree method in financial engineering

... Finite Difference Methods in Financial Engineering A Partial Differential Equation Approach Daniel J Duffy Finite Difference Methods in Financial Engineering For other titles in the Wiley Finance ... IMPLEMENTATION IN C++ 30 Finding the Appropriate Finite Difference Schemes for your Financial Engineering Problem 30.1 Introduction and objectives 30.2 The financial model 30.3 The viewpoints in the continuous ... equations in quantitative finance 8 Finite Difference Methods in Financial Engineering 1.2 TWO-POINT BOUNDARY VALUE PROBLEM Let us examine a general second-order ordinary differential equation given in...

Ngày tải lên: 23/01/2014, 06:20

... in Reservoir Engineering singularity in velocity at both ends of the fracture; the expression √(1-x2 ) appears in the denominator, leading to infinite tip velocities The integral in Equation 2-65 ... formation invasion, and time-lapse well logging using drilling data In terms of techniques, we introduce modern ideas in singular integral equations, improper integrals, advanced conformal mapping, ... addresses the inefficiencies just pointed out, bringing the power of singular integral equations, linear superposition, conformal mapping, modern curvilinear grid generation, moving boundary value...

Ngày tải lên: 23/06/2014, 17:46

... Finite Difference Methods in Financial Engineering A Partial Differential Equation Approach Daniel J Duffy Finite Difference Methods in Financial Engineering For other titles in the Wiley Finance ... IMPLEMENTATION IN C++ 30 Finding the Appropriate Finite Difference Schemes for your Financial Engineering Problem 30.1 Introduction and objectives 30.2 The financial model 30.3 The viewpoints in the continuous ... equations in quantitative finance 8 Finite Difference Methods in Financial Engineering 1.2 TWO-POINT BOUNDARY VALUE PROBLEM Let us examine a general second-order ordinary differential equation given in...

Ngày tải lên: 27/06/2014, 22:20

... derivation of system equations, including the various methods of incorporating the boundary conditions, are indicated in Chapter The solutions of finite element equations arising in equilibrium, eigenvalue, ... improved by taking more node points in the beam 1.6.7 Finite Element Method of Numerical Solution (Displacement Method) In the finite element method, we divide the given structure (beam) into several ... programming languages are being developed The use of personal computers and workstations in engineering analysis and design is becoming increasingly popular as the price of hardware is decreasing...

Ngày tải lên: 08/04/2014, 10:36

... exponent in the kinetic equations, particularly in small grain size 582 Applications of Monte Carlo Method in Science and Engineering regimes (i.e., for grain sizes ranging from to 15 lattice spacing ... phase lattice points can be arranged either in the form of grain inclusions, whiskers, 566 Applications of Monte Carlo Method in Science and Engineering fibers The influence of the input parameters ... the cylindrical cluster using H1=HJ+HD+HA_macro+HB including the macroscopic anisotropy and H2=HJ+HD+HA_micro+HB 548 Applications of Monte Carlo Method in Science and Engineering including the...

Ngày tải lên: 29/06/2014, 13:20

... 2011 Printed in India A free online edition of this book is available at www.intechopen.com Additional hard copies can be obtained from orders@intechweb.org Applications of Monte Carlo Method in ... of Monte Carlo Method in Science and Engineering describe the X-ray absorption and scattering as well as the electron drift which leads to image blurring Measuring X-rays with scintillation detectors ... Simulations in NDT 13 Fig 10 Method for determining the BSR using the intensity profile along the BSR462-5 double wire specimen 3.2.1.1 BSR test results BSR images were obtained using the following simulation...

Ngày tải lên: 29/06/2014, 13:20

... unpinned, 638 Wiener path integral Brownian motion, 635 Worldline, 204 Wronskian Bessel functions, 95 linear independence, 41 679 MATHEMATICAL METHODS IN SCIENCE AND ENGINEERING This Page Intentionally ... of Diflerintegrals in Science and Engineering 14.7.1 Continuous Time Random Walk (CTRW) 14.7.2 Fractional Fokker-Planck Equations Problems 15 INFINITE SERIES 15.1 Convergence of Infinite Series ... and Integral 385 Operations for Integer Orders Differintegrals 385 14.2.1 Griinwald’s Definition of Differintegrals 385 14.2.2 Riemann-Liouville Definition of Differintegrals 387 Other Definitions...

Ngày tải lên: 13/08/2014, 09:21

... emerging field with enormous potential and with applications to physics, chemistry, biology, engineering, and finance For beginning researchers and instructors who want to add something new and interesting ... complex integrals, series, and analytic continuation along with the methods of evaluating some definite integrals Chapter 14 introduces the basics of fractional calculus After introducing xxiv ... considered an integral part of the learning process In a vast area like mathematical methods in science and engineering, there is always room for new approaches, new applications, and new topics In fact,...

Ngày tải lên: 13/08/2014, 09:21

... takes integer values = 0,1,2 i) Examine the nature of the singular point at z = 00 ii) Show that in t h e limit as x 00, the solution goes as f iii) Using the Frobenius method, find a n infinite ... differential equation into the form It is clear that the singularity at infinity is essential Because it is a t the end point of our interval it does not pose any difficulty in finding a series solution ... solution must be finite in the entire interval [O,w]; hence we terminate the series after a finite number of terms This is accomplished by restricting the energy of the system to certain integer values...

Ngày tải lên: 13/08/2014, 09:21

... main reason for our interest in hypergeometric functions is that so many of the second-order linear ordinary differential equations encountered in physics and engineering can be expressed in ... integrated term is zero Integrating the second term in Equation (8.18) by parts again and using the boundary condition (8.15) we see that the integrated term is again zero, thus obtaining lbu* (pu’)’dx ... equations in physics and engineering can be solved by the method of separation of variables This method helps us to reduce a second-order partial differential equation into a set of ordinary differential...

Ngày tải lên: 13/08/2014, 09:21

... could write 4 = (Iml+ $2 (9.142) Again from the conclusions of Theorem IV there exists a minimum value, mmin, thus determining X as X = mmin (9.143) To find mminwe equate the two expressions [Eqs ... o obtain (9.144) mmin -1 = (9.146) Since m changes by integer amounts, we could write h i n = mmax integer - -1 = - integer 21 = integer (9.147) This equation says that could only take integer ... corresponding t o a given r ( z ,m) are known For m > 0, depending on whether p ( m ) is a n increasing or a decreasing function, there are two cases 9.4.1 Case I ( m > and p ( m ) is an increasing...

Ngày tải lên: 13/08/2014, 09:21

... cos+cos - cos8 sin +sin cos - cos 6sin +cos sin sin - sin + (10.56) (10.57) ++ + + cos+ sin cos8cos+sin sin cos 6cos +cos -sin 8cos q5 - sin + ++ The inverse of A is A-l = x sin+sin6 cos +sin cos (10.58) ... about the xl-axis as cosdsin+ cosCp -sin4 - sin $ sin4cos$ cos~cos$ Reversing the order we get R2R1 = [ (10.93) - sin $ cos Cp cos $ sin $ sin Cp cos Cp sin sin $ - cos sin q5 cos $ cos (10.94) ... COORDINATES In threedimensional Euclidean space a Cartesian coordinate system can be constructed by choosing three mutually orthogonal straight lines A point is defined by giving its coordinates,...

Ngày tải lên: 13/08/2014, 09:21

... operator in spherical polar coordinates 10.23 Write the Laplace operator in cylindrical coordinates 10.24 In four dimensions spherical polar coordinates (r, 6,Q,) are defined x, as x y z = rsinxsinBcosQ, ... general linear transformation [Eq (10.250)] matrix elements a$ can be obtained by using dZa a; = - dxp (10.277) In Minkowski spacetime the distance between two infinitesimally close points (events) ... Groups with infinite number of elements like R(n)are called infinite groups A group with finite number of elements is called a finite group, where the number of elements in a finite group is...

Ngày tải lên: 13/08/2014, 09:21

... remaining two rotations are performed about different sets of axis Because we are interested in evaluating RWz,y, z ) = WZ’,Y’, 4, ( 11.207) where (z,y, z ) and (z’,y’, z ’ ) are two points in ... interested in expressing the operator R in terms of the ( z ~ , zn) coordinates Action yn, of R on the coordinates induces the following change in @(z, z ) : y, 252 CONTINUOUS GROUPS AND REPRESENTATIONS ... (11.279) Using the matrix elements of (Ly)n obtained in Section 11.11.7, we write this as dm,,(P) = Jmmg - i ( L g ) m m , =[: i I;f 0 :I isinP[ 1/2 -l/2 i -1/2 1/2 Finally adding these we find d...

Ngày tải lên: 13/08/2014, 09:21

... equation in two dimensions The method of analytic continuation is very useful in finding solutions of differential equations and evaluating some definite integrals Infinite series, infinite products, ... corresponding points approach t h e same point in the z-plane, they are mapped to different points in the w-plane For points D and E t h e function is again single valued For this case the cut lines ... one-to-one mappings, that is, a single point in the z-plane is mapped to a single point in the w-plane Example 12.7 Two-to-one mapping: We now consider the function w = z2 (12.81) and write it in plane...

Ngày tải lên: 13/08/2014, 09:21

... analytic continuation 13.7 COMPLEX TECHNIQUES IN TAKING SOME DEFINITE INTEGRALS Many of the definite integrals encountered in physics and engineering can be evaluated by using the complex integral ... 0, is called a singular point of order m Definition I11 Essential singular point: If m is infinity, then singular point a is called an essential Definition IV Simple Pole: In Definition 11, if ... CLASSIFICATION OF SINGULAR POINTS 13.4 347 CLASSIFICATION OF SINGULAR POINTS Using Laurent the series we can classify singular points of a function Definition I Isolated singular point: If a function...

Ngày tải lên: 13/08/2014, 09:21

... first integrating up to an infinitesimally close point, ( a - a), to a and then continue integration on the other side from an arbitrarily close point, ( a + S), to infinity, that is, define the integral ... TECHNIQUES IN TAKING SOME DEFINITE INTEGRALS 355 f i g 13.14 Contour for Example 13.6 where C is a semicircle in the upper half of the z-plane considered in the limit as the radius goes t o infinity ... Cauchy principal value integral we can evaluate the Cauchy principal value of the integral (13.174) by using the contour in Figure 13.18 In this case we write (13.177) z] and evaluate this integral...

Ngày tải lên: 13/08/2014, 09:21

... in finding solutions of extraordinary differential equations can now be used in Equation (14.158) to compose differintegrals Another useful formula is obtained when Q takes integer values N in ... difficulty in experimentally defining the value of dq-l f (O+), t h e Caputo definition has also found some t h e initial condition dxq use in the literature 4.8 Show the differintegral 15 INFINITE ... of functions and in particular t o power series We then introduce some analytic techniques for finding infinite sums We also discuss asymptotic series and infinite products In conjunction with...

Ngày tải lên: 13/08/2014, 09:21

... function with infinitely many roots can be expressed as an infinite product We can find the infinite product representations of the sine and cosine functions using complex analysis: In the z-plane ... I I N Y (N+ In) (-1- i ) I N+1 ) (N+ (1 -I) In) Fig 15.3 Contour for finding series sums using the residue theorem 15.9.3 Using Residue Theorem to Sum infinite Series Some of the infinite series ... INFINITE PRODUCTS 471 Integrating Equation (15.223) gives and finally the general expression is obtained as (15.225) Applying this formula with z = x to the sine and cosine functions we obtain...

Ngày tải lên: 13/08/2014, 09:21

... useful in representing a function in a finite interval, like [0,27r] or [-L, L ] , or a periodic function in the infinite interval (-CO,CO) We now consider a nonperiodic function in the infinite interval ... finite wave train: We now find the Fourier transform of a finite wave train, which is given as (16.44) For N = this wave train is shown in Figure 16.1 I Since f ( t ) is an odd function we find ... Transforms in Three Dimensions Fourier transforms can also be defined in three dimensions as Substituting Equation (16.68) back in Equation (16.69) and interchanging the order of integration we obtain...

Ngày tải lên: 13/08/2014, 09:21