Partial differential equation

(BQ) Ebook Analytical and computational methods of advanced engineering mathematics: Part 1 includes the following content: Chapter 1 FirstOrder ODEs; chapter 2 SecondOrder Linear ODEs; chapter 3 Higher Order Linear ODEs; chapter 4 Systems of ODEs, Phase Plane, Qualitative Methods; chapter 5 Series Solutions of ODEs, Special Functions; chapter 6 Laplace Transforms; chapter 7 Linear Algebra: Matrices, Vectors, Determinants, Linear Systems; chapter 8 Linear Algebra: Matrix Eigenvalue Problems; chapter 9 Vector Differential Calculus, Grad, Div, Curl; chapter 10 Vector Integral Calculus, Inte...
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(BQ) Ebook Numerical recipes in Fortran 77: The art of scientific computing (Volume 1 of Fortran Numerical recipes) – Part 2 presents the following content: Fast fourier transform, fourier and spectral applications, statistical description of data, modeling of data, integration of ordinary differential equations, two point boundary value problems, integral equations and inverse theory, partial differential equations, lessnumerical algorithms.
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The paper "Integral boundary value problem for fuzzy partial hyperbolic differential equations" presents some new results on the existence and uniqueness of fuzzy solutions for some classes of fuzzy partial hyperbolic differential equations with integral boundary conditions. Our results are demonstrated in some computational examples. In this we use the same strategy as BuckleyFeuring to build fuzzy solutions from fuzzifying the deterministic solutions.
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In the paper "On the existence of fuzzy solutions for partial hyperbolic functional differential equations", we consider the boundary valued problems for fuzzy partial hyperbolic functional differential equations with local and integral boundary conditions. A new weighted metric is used to investigate the existence and uniqueness of fuzzy solutions for these problems in a complete fuzzy metric space. Our results are demonstrated in some numerical examples in which we use the same strategy as BuckleyFeuring to build fuzzy solutions from fuzzifying the deterministic solutions.
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The classical TriebelLizorkin spaces on Euclidean spaces Rn, considered as generalizations of other classical spaces such as Lesbegue spaces, BMO spaces, Hardy spaces, and Sobolev spaces, are essential in approximation theory and partial differential equations.
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Lecture Mathematics III. After completing this section, you will understand knowledge about: partial differential equation of first order, Linear partial differential equation, Nonlinear partial differential equation, Homogenous and nonhomogeneous partial differential equation with constant coefficient, Cauchy type, Monge’s method, Second order partial differential equation.
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In this study, we investigated one of the most popular stochastic volatility pricing models, the Heston model, for European options. This paper deals with the implementation of a finite difference scheme to solve a twodimensional partial differential equation form of the Heston model.
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Bài viết này trình bày một phương pháp giải phương trình đạo hàm riêng (partial differential equation  PDE) thoả điều kiện biên Dirichlete sử dụng mạng neural truyền thẳng một lớp ẩn (singlehidden layer feedfordward neural networks  SLFN) gọi là phương pháp mạng neural (neural network method – NNM). Các tham số của mạng neural được xác định dựa trên thuật toán huấn luyện mạng lan truyền ngược (backpropagation  BP). Kết quả nghiệm PDE thu được bằng phương pháp NNM chính xác hơn so với nghiệm PDE giải bằng phương pháp sai phân hữu hạn.
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The objectives of this dissertation are to study the asymptotic behavior of solutions of these nonlocal problems via the existence of (its finite dimensional) global attractors, and the existence and exponential stability of stationary solutions.
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The objectives of this dissertation are to study the asymptotic behavior of solutions of these nonlocal problems via existence of (its finite dimensional) global attractors, and the existence and exponential stability of stationary solutions.
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The dynamic response to variable magnitude moving distributed masses of simply supported nonuniform Bernoulli–Euler beam resting on Pasternak elastic foundation is investigated in this paper. The problem is governed by fourth order partial differential equation with variable and singular coefficients. The main objective of this work is to obtain closed form solution to this class of dynamical problem.
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Consider a stochastic evolution equation containing Stratonovichmultiplicative white noise of the form ( , ) du Au f t u u W dt where the partial differential operator A is positive definite, selfadjoint with a discrete spectrum; and the nonlinear part f satisfies the Lipschitz condition with belonging to an admissible function space. We prove the existence of a (stochastic) inertial manifold for the solutions to the above equation. Our method relies on the LyapunovPerron equation in a combination with the admissibility of function spaces.
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In this paper, we investigate the existence and uniqueness of fuzzy solution for a class of general hyperbolic equations with statedependent delays. We will prove the wellposedness of problem doesn’t depend on the domain and boundary data as well as initial data. Our method is based on Banach fixed point theorem in completely new weighted metric space.
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We introduce several weighted Lp(R+)norm inequalities and integral transform related to the generalized convolution with a weight function for the Fourier cosine and Laplace transforms. Some applications of these inequalities to estimate the solutions of some partial differential equations are considered.
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In this paper, we study the existence and uniqueness of fuzzy solutions for general hyperbolic partial differential equations with local conditions making use of the Banach fixed point theorem. Some examples are presented to illustrate our results.
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In present time significant attention has been given to study noninteger order partial differential equations. The current article is devoted to find numerical solutions to the following class of time–space fractional partial differential.
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Motivated by the fact that the fractional Laplacean generates a wider choice of the interpolation curves than the Laplacean or biLaplacean, we propose a new nonlocal partial differential equation inspired by the CahnHilliard model for recovering damaged parts of an image. We also note that our model is linear and that the computational costs are lower than those for the standard CahnHilliard equation, while the inpainting results remain of high quality.
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This paper studies the active damping of the oscillations of lightly damped linear systems whose parameters are indeterminate or may change through time. Systems with an arbitrary number of vibration modes are considered. Systems described by partial differential equations, that yield an infinite number of vibration modes, can also be included. In the case of collocated feedback, i.e. the sensor is placed at the same location of the actuator, a simple fractional order differentiation or integration of the measured signal is proposed that provides an effective control.
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This paper first shows that this geometric distribution is only a particular distribution case and that many other distributions (an infinity) are in fact possible. From the networks obtained, a class of partial differential equations (heat equation with a spatially variable coefficient) is then deduced. This class of equations is thus another tool for power law type long memory behaviour modelling, that solves the drawback inherent in fractional heat equations that was proposed to model anomalous diffusion phenomena.
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The present paper is concerned to analyse the magnetohydrodynamic (MHD) Casson fluid flow free convection boundary layer flow of an incompressible electrically conducting fluid through a porous medium subjected to magnetic field in the presence of radiation and chemical reaction. Similarity variables are used to transform the nonlinear governing equations are reduced to ordinary partial differential equations, solved by shooting process with BVP4C
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