[PDF] Top 20 Numerical Methods for Solving the Inverse Problem of Parameter Identification in Parabolic and Fourth-Order Partial Differential Equations

... Introduction There is a broad range of mathematical problems that can be classified under the title of inverse problems. Their main overarching commonality is they involve converting a set of observations of a ... See full document

... convert parabolic PDEs to ordinary differential equations or even to algebraic ...this problem are presented in literature. Several numerical methods have been proposed for the ... See full document

... for the orders 1, 2, 3 and 12% for the fourth order [16]. The ODE15s solver is based on the NDFs of order 1 to 5 [16]. The order 5 NDF is used as default method in the code. As an option, it ... See full document

... Mesh-based numerical techniques are not feasible, however, for solving mathematical problems defined in spaces of high dimensions (higher than ...the problem [ 11 ...nonlinear parabolic PDEs in ... See full document

... to fourth-order PDEs are necessary to know the qualitative behav- ior of natural processes and physical ...most fourth-order time-dependent PDEs have no closed-form solutions except for ... See full document

... by solving a system on a coarse grid and after that interpolating the solution to develop the initial guess on a fine ...Multigrid methods begin from this idea but make greater use of the available ...for ... See full document

... fractional order in mathematical models has become increasingly in ...fractional order derivative include specific properties of the process are reformu- lating the integer order of the diffussion, ... See full document

... Block methods based on newton interpolations for solving special second order ordinary differential equations ...(1991). Numerical methods for ordinary differential ... See full document

... of parabolic partial differential equations with source control ...of equations arise, for example, in the study of heat conduction processes, thermoelasticity, chem- ical diffusion and control ... See full document

... new numerical method for obtaining smooth approximations for solving ho- mogeneous and nonhomogeneous parabolic partial differential equations based on nonpolynomial cubic ... See full document

... first-order equations, to our knowledge, leads to serious computational burden as well as wastage in computer ...formulate numerical algorithms capable of solving problem ...differing ... See full document

... including partial differential equations (PDEs), integral and integro-differential equa- tions and ...the numerical solution of fractional fourth order integro-differential ...the ... See full document

... considerer parabolic partial differential equations: w t − ( ) w x x = r x t ( ) , under the conditions w a t ( 1 , ) = k t 1 ( ) w b t ( ) 1 , = k 2 ( ) t , w x a ( , 2 ) = h t 1 ( ) on a ... See full document

... higher order numerical methods for solving fractional differential ...fractional differential operator: we obtain a numerical method for solving a linear fractional ... See full document

... accuracy order. Furthermore, an explicit method for solving FDEs has several problems with some fractional ...a problem of stability with a small fractional order and a problem of low ... See full document

... (8.1f) We aim to incorporate the treatment of Dirichlet boundary conditions into our finite el- ement C++ code. For this reason, now you are required to implement a class BoundaryDofs which will take care to detect and ... See full document

... The problem of determining unknown coefficients in parabolic partial differential equa- tions has been treated by many authors [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], and among the most versatile ... See full document

... the equations is particularly important when deal- ing with problems admitting shocks or other discontinuities in the solution, ...when solving the hydrodynamical ...the equations are not written in ... See full document

... linear partial differential equations of first order ( ) ( ) ( ) ( ) x t ( ) ( ) ( ) a x t w , x t , + b x t w , x t , = h x t w x t , , + r x t , on a region E = ( a b 1 , 1 ) ( × a b 2 , 2 ) ... See full document

... The inverse problem of identifying an unknown source control parameter in a semilinear parabolic equation under an inte- gral overdetermination condition is ...proposed problem is ... See full document