Solution of Cauchy Problems by the Multiple Scale Method of Particular Solutions Using Polynomial Basis Functions

A strong-form meshfree computational method for plane elastostatic equations of anisotropic functionally graded materials via multiple-scale Pascal polynomials, Polynomial Particular Solutions for the Solutions of PDEs with Variables Coefficients, Learning solutions to the source inverse problem of wave equations using LS-SVM

Regularization tools

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The plane wave method for inverse problems associated with Helmholtz-type equations
A modified collocation Trefftz method for the inverse Cauchy problem of Laplace equation
A regularization method for the approximate particular solution of nonhomogeneous Cauchy problems of elliptic partial differential equations with variable coefficients
Fast simulation of multi-dimensional wave problems by the sparse scheme of the method of fundamental solutions
A new investigation into regularization techniques for the method of fundamental solutions
A multiple-scale Pascal polynomial for 2D Stokes and inverse Cauchy-Stokes problems
A meshless method for solving the Cauchy problem in three-dimensional elastostatics
The method of fundamental solutions for inverse boundary value problems associated with the two-dimensional biharmonic equation
Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems
An alternating iterative algorithm for the Cauchy problem associated to the Helmholtz equation
A BEM formulation in conjunction with parametric equation approach for three-dimensional Cauchy problems of steady heat conduction
The method of approximate particular solutions for the time-fractional diffusion equation with a non-local boundary condition
Numerical solution of an inverse reaction-diffusion problem via collocation method based on radial basis functions
Polynomial particular solutions for solving elliptic partial differential equations
A meshless method for the numerical solution of a two-dimension IHCP
Localized method of approximate particular solutions for solving unsteady Navier-Stokes problem
Method of particular solutions using polynomial basis functions for the simulation of plate bending vibration problems
Numerical solution of the Cauchy problem for steady-state heat transfer in two-dimensional functionally graded materials
A multiple-scale Trefftz method for an incomplete Cauchy problem of biharmonic equation
Numerical solution of the Laplacian Cauchy problem by using a better postconditioning collocation Trefftz method
The method of approximate particular solutions for solving certain partial differential equations
Dual reciprocity boundary element method solution of the Cauchy problem for Helmholtz-type equations with variable coefficients
A survey of applications of the MFS to inverse problems
Least-square-based radial basis collocation method for solving inverse problems of Laplace equation from noisy data
The method of particular solutions for solving scalar wave equations
Numerical approximation of the one-dimensional inverse Cauchy–Stefan problem using a method of fundamental solutions
Boundary knot method for some inverse problems associated with the Helmholtz equation
The cauchy problem for the critical nonlinear Schrödinger equation in Hs
Analysis of Discrete Ill-Posed Problems by Means of the L-Curve
An inverse problem in corrosion detection
A radial basis meshless method for solving inverse boundary value problems
Application of radial basis meshless methods to direct and inverse biharmonic boundary value problems
Inverse Problem Theory and Methods for Model Parameter Estimation
Simulation of Seismic Wave Scattering by Embedded Cavities in an Elastic Half-Plane Using the Novel Singular Boundary Method
State estimation and inverse problems in electrical impedance tomography: observability, convergence and regularization
The radial basis functions method for identifying an unknown parameter in a parabolic equation with overspecified data
Reconstruction of the Shape and Surface Impedance from Acoustic Scattering Data for an Arbitrary Cylinder