Numerical Methods of Solving PDEs
An ALE ESFEM for solving PDEs on evolving surfaces
... Abstract. Numerical methods for approximating the solution of partial differential equations on evolving hypersurfaces using surface finite ele- ments on evolving triangulated surfaces are ...velocity. ...
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High-resolution method for numerically solving PDEs in process engineering
... numerically solving PDEs with Cauchy or Neu- mann boundary conditions have been developed in this ...convergent numerical solutions have been obtained for the test ...developed methods are ...
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Adaptive numerical methods for PDEs
... Adaptive methods are an important tool for numerically solving Partial Differential Equations ...adaptive numerical algorithms have been suggested for both elliptic equations and time varying ...
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Tensor numerical methods for multidimensional PDES: theoretical analysis and initial applications
... tensor numerical methods for multidimen- sional stationary and time-dependent partial differential equations ...parametric PDEs, and to dynamical equations arising in scientific ...traditional ...
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Efficient Method for Solving Fourth Order PDEs
... order PDEs, HPM, LA-transform, He's ...efficient methods have been proposed by many researchers for obtaining analytic, approximate and numerical ...
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Multiscale RBF collocation for solving PDEs on spheres
... used widely. Examples include [1, 6, 9, 10]. For boundary value problems, the technique predominantly used in the literature, with the exception of [23], where a Galerkin method was used, has been collocation, mainly be- ...
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Solving systems of hyperbolic PDEs using multiple GPUs
... Chapter 1 Introduction “The Road goes ever on and on Down from the door where it began.” — Bilbo Baggins (J. R. R. Tolkien) This master thesis contains several topics of interest, where the main areas are parallel ...
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An Analytical and Numerical Study of a Class of Nonlinear Evolutionary PDEs.
... In numerical analysis and computational fluid dynamics, Godunov’s scheme is a conserva- tive numerical scheme, suggested by ...for solving partial differential ...volume methods solves exact, ...
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On space–time adaptive schemes for the numerical solution of PDEs
... by solving adjoint problems ...refinement methods, Harten developed first multiresolution based schemes (MR) for conservation laws [19, ...MR methods is to control the truncation error by estimating ...
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A Probabilistic Numerical Method for Fully Nonlinear Parabolic PDEs
... related numerical methods based on finite differences in the context of Hamilton-Jacobi-Bellman nonlinear PDEs: • Bonnans and Zidani [8] introduced a finite difference scheme which satisfies the ...
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Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopy
... iterative methods, we use the frozen Jacobian at the initial guess, and we employ its LU factors repeatedly in the multi-step part to solve the related lower and upper triangular ...such methods is limited. ...
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An efficient approach for solving a class of nonlinear 2D parabolic PDEs
... for solving 2D problems. We compare three different methods: two iterations of New- ton’s method (denoted by N in tables and figures), and the linearization method, first in its standard form (denoted by L), ...
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An efficient indirect RBFN-based method for numerical solution of PDEs
... In solving the Navier-Stokes equations for two dimensional flows, numerical methods usually employ the stream function-vorticity formulation rather than the velocity- pressure ...
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Study the Numerical Methods for Solving Syste...
... on numerical methods for solving ordinary differential ...for solving the ordinary differential equation using Euler and Runge Kutta 4 th order ...on numerical methods for ...
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Numerical Methods for Solving Systems of Nonlinear Equations
... that numerical methods are a vital strand of math- ...only solving nonlinear algebraic equations with one variable, but also systems of nonlinear algebraic ...of numerical meth- ods in order ...
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Numerical Methods for Solving Fractional Differential Equations
... for solving FDEs has several problems with some fractional ...enhanced methods for each ...Several numerical examples are demonstrated to show the e↵ectiveness for the proposed ...
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Numerical methods for solving wave scattering problems
... The author is deeply grateful to his academic advisor, Professor Alexander G. Ramm, for his excellent advice, teaching, and guidance throughout the years. Most of mathematical analysis knowledge that the author has ...
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Deep Learning-Based Numerical Methods for High-Dimensional Parabolic PDEs and BSDEs
... learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations”. In: Communications in Mathematics and Stat[r] ...
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Solving partial differential equations (PDEs)
... For ordinary differential equations (ODEs), we need to know the initial value(s) to be able to compute a solution. For partial differential equations (PDEs), we need to know the initial values and extra ...
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Efficient Numerical Methods for Solving Differential Algebraic Equations
... DAEs can be transformed into ODE problems via differentiation. The number of differentiations needed in the transforming process is called the differentiation index. This number can describe some characteristics of the ...
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