Conformal mapping and bipolar coordinate for eccentric Laplace problems. - Jeng-Tzong Chen; Ming-Hong Tsai; Chein-Shan Liu (Comput. Appl. Eng. Educ., 2009)

An inverse problem for computing a leading coefficient in the Sturm-Liouville operator by using the boundary data. - Chein-Shan Liu (Appl. Math. Comput., 2011)

Optimally scaled vector regularization method to solve ill-posed linear problems. - Chein-Shan Liu (Appl. Math. Comput., 2012)

Computing the eigenvalues of the generalized Sturm-Liouville problems based on the Lie-group SL(2, R). - Chein-Shan Liu (J. Comput. Appl. Math., 2012)

Adaptive multilayer method of fundamental solutions using a weighted greedy QR decomposition for the Laplace equation. - Takemi Shigeta; D. L. Young; Chein-Shan Liu (J. Comput. Phys., 2012)

The Lie-Group Shooting Method for Solving Multi-dimensional Nonlinear Boundary Value Problems. - Chein-Shan Liu (J. Optim. Theory Appl., 2012)

A Lie-group DSO(n)DSO(n) method for nonlinear dynamical systems. - Chein-Shan Liu (Appl. Math. Lett., 2013)

Developing an SL(2, R) Lie-group shooting method for a singular ϕ-Laplacian in a nonlinear ODE. - Chein-Shan Liu (Commun. Nonlinear Sci. Numer. Simul., 2013)

Solving Nonlinear Differential Algebraic Equations by an Implicit GL(n, R) Lie-Group Method. - Chein-Shan Liu (J. Appl. Math., 2013)

An Optimally Generalized Steepest-Descent Algorithm for Solving Ill-Posed Linear Systems. - Chein-Shan Liu (J. Appl. Math., 2013)

A Third-Order p-Laplacian Boundary Value Problem Solved by an SL(3, ℝ) Lie-Group Shooting Method. - Chein-Shan Liu (J. Appl. Math., 2013)

A maximal projection solution of ill-posed linear system in a column subspace, better than the least squares solution. - Chein-Shan Liu (Comput. Math. Appl., 2014)

A new sliding control strategy for nonlinear system solved by the Lie-group differential algebraic equation method. - Chein-Shan Liu (Commun. Nonlinear Sci. Numer. Simul., 2014)

Optimal Algorithms and the BFGS Updating Techniques for Solving Unconstrained Nonlinear Minimization Problems. - Chein-Shan Liu (J. Appl. Math., 2014)

The Solution of SO(3) through a Single Parameter ODE. - Chein-Shan Liu (J. Appl. Math., 2014)

A globally optimal tri-vector method to solve an ill-posed linear system. - Chein-Shan Liu (J. Comput. Appl. Math., 2014)

A doubly optimized solution of linear equations system expressed in an affine Krylov subspace. - Chein-Shan Liu (J. Comput. Appl. Math., 2014)

A double optimal iterative algorithm in an affine Krylov subspace for solving nonlinear algebraic equations. - Chein-Shan Liu (Comput. Math. Appl., 2015)

A novel Lie-group theory and complexity of nonlinear dynamical systems. - Chein-Shan Liu (Commun. Nonlinear Sci. Numer. Simul., 2015)

A new regularized boundary integral equation for three-dimensional potential gradient field. - Wenzhen Qu; Yaoming Zhang; Chein-Shan Liu (Adv. Eng. Softw., 2016)

Fast simulation of multi-dimensional wave problems by the sparse scheme of the method of fundamental solutions. - Ji Lin 001; C. S. Chen; Chein-Shan Liu; Jun Lu 007 (Comput. Math. Appl., 2016)

A fast multiple-scale polynomial solution for the inverse Cauchy problem of elasticity in an arbitrary plane domain. - Chein-Shan Liu (Comput. Math. Appl., 2016)

A multiple-direction Trefftz method for solving the multi-dimensional wave equation in an arbitrary spatial domain. - Chein-Shan Liu; Chung-Lun Kuo (J. Comput. Phys., 2016)

A multiple-scale Pascal polynomial for 2D Stokes and inverse Cauchy-Stokes problems. - Chein-Shan Liu; D. L. Young (J. Comput. Phys., 2016)

An iterative method based-on eigenfunctions and adjoint eigenfunctions for solving the Falkner-Skan equation. - Chein-Shan Liu (Appl. Math. Lett., 2017)

Reconstructing a second-order Sturm-Liouville operator by an energetic boundary function iterative method. - Chein-Shan Liu; Botong Li (Appl. Math. Lett., 2017)

Solving a singular beam equation by using a weak-form integral equation method. - Chein-Shan Liu; Dongjie Liu; Wun-Sin Jhao (Appl. Math. Lett., 2017)

The polynomial Trefftz method for solving backward and inverse source wave problems. - Chein-Shan Liu (J. Comput. Appl. Math., 2017)

An iterative method based on coupled closed-form coefficients expansions for recovering the pollutant source and initial pollution profile. - Chein-Shan Liu; Peifang Wang; Jiang-Ren Chang (J. Comput. Appl. Math., 2017)

Solving singularly perturbed problems by a weak-form integral equation with exponential trial functions. - Chein-Shan Liu (Appl. Math. Comput., 2018)

Recovering a source term in the time-fractional Burgers equation by an energy boundary functional equation. - Chein-Shan Liu; Jiang-Ren Chang (Appl. Math. Lett., 2018)

Solving nonlinear singularly perturbed problems by fractional order exponential trial functions. - Chein-Shan Liu; Chih-Wen Chang (Appl. Math. Lett., 2018)

Optimal shape parameter in the MQ-RBF by minimizing an energy gap functional. - Chein-Shan Liu; Dongjie Liu (Appl. Math. Lett., 2018)

Trefftz energy method for solving the Cauchy problem of the Laplace equation. - Chein-Shan Liu; Fajie Wang; Yan Gu 007 (Appl. Math. Lett., 2018)

Boundary function method for inverse geometry problem in two-dimensional anisotropic heat conduction equation. - Fajie Wang; Qingsong Hua; Chein-Shan Liu (Appl. Math. Lett., 2018)

Optimal sources in the MFS by minimizing a new merit function: Energy gap functional. - Fajie Wang; Chein-Shan Liu; Wenzhen Qu (Appl. Math. Lett., 2018)

An energy method of fundamental solutions for solving the inverse Cauchy problems of the Laplace equation. - Chein-Shan Liu; Fajie Wang (Comput. Math. Appl., 2018)

A meshless method for solving the nonlinear inverse Cauchy problem of elliptic type equation in a doubly-connected domain. - Chein-Shan Liu; Fajie Wang (Comput. Math. Appl., 2018)

A novel Trefftz method for solving the multi-dimensional direct and Cauchy problems of Laplace equation in an arbitrary domain. - Ji Lin 001; Chein-Shan Liu; Wen Chen 003; Linlin Sun (J. Comput. Sci., 2018)

Closed-form higher-order numerical differentiators for differentiating noisy signals. - Chein-Shan Liu; Leiting Dong (Appl. Math. Comput., 2019)

Solving the inverse conductivity problems of nonlinear elliptic equations by the superposition of homogenization functions method. - Chein-Shan Liu; Chih-Wen Chang (Appl. Math. Lett., 2019)

Nonlinear wave inverse source problem solved by a method of m-order homogenization functions. - Chein-Shan Liu; Lin Qiu; Fajie Wang (Appl. Math. Lett., 2019)

A Trefftz/MFS mixed-type method to solve the Cauchy problem of the Laplace equation. - Chein-Shan Liu; Fajie Wang; Yan Gu 007 (Appl. Math. Lett., 2019)

An energy regularization of the MQ-RBF method for solving the Cauchy problems of diffusion-convection-reaction equations. - Chein-Shan Liu; Chih-Wen Chang (Commun. Nonlinear Sci. Numer. Simul., 2019)

The periods and periodic solutions of nonlinear jerk equations solved by an iterative algorithm based on a shape function method. - Chein-Shan Liu; Jiang-Ren Chang (Appl. Math. Lett., 2020)

Forced and free vibrations of composite beams solved by an energetic boundary functions collocation method. - Chein-Shan Liu; Botong Li (Math. Comput. Simul., 2020)

A boundary collocation method for anomalous heat conduction analysis in functionally graded materials. - Zhuo-Jia Fu; Li-Wen Yang; Qiang Xi; Chein-Shan Liu (Comput. Math. Appl., 2021)

Three novel fifth-order iterative schemes for solving nonlinear equations. - Chein-Shan Liu; Essam Roshdy El-Zahar; Chih-Wen Chang (Math. Comput. Simul., 2021)

A boundary shape function iterative method for solving nonlinear singular boundary value problems. - Chein-Shan Liu; Essam Roshdy El-Zahar; Chih-Wen Chang (Math. Comput. Simul., 2021)

A splitting method to solve a single nonlinear equation with derivative-free iterative schemes. - Chein-Shan Liu; Hong-Ki Hong; Tsung-Lin Lee (Math. Comput. Simul., 2021)

Solving a singular beam equation by the method of energy boundary functions. - Chein-Shan Liu; Botong Li (Math. Comput. Simul., 2021)

Boundary shape function iterative method for nonlinear second-order boundary value problems with nonlinear boundary conditions. - Aimin Deng; Ji Lin 001; Chein-Shan Liu (Math. Comput. Simul., 2022)

Modified asymptotic solutions for second-order nonlinear singularly perturbed boundary value problems. - Chein-Shan Liu; Chih-Wen Chang (Math. Comput. Simul., 2022)

Two-point generalized Hermite interpolation: Double-weight function and functional recursion methods for solving nonlinear equations. - Dongjie Liu; Chein-Shan Liu (Math. Comput. Simul., 2022)

Lie-Group Shooting/Boundary Shape Function Methods for Solving Nonlinear Boundary Value Problems. - Chein-Shan Liu; Chih-Wen Chang (Symmetry, 2022)

Periodic Orbits of Nonlinear Ordinary Differential Equations Computed by a Boundary Shape Function Method. - Chein-Shan Liu; Chih-Wen Chang; Yung-Wei Chen; Yen-Shen Chang (Symmetry, 2022)

Solving Sturm-Liouville inverse problems by an orthogonalized enhanced boundary function method and a product formula for symmetric potential. - Chein-Shan Liu; Botong Li (Math. Comput. Simul., 2023)

Solving Nonlinear Elliptic Inverse Source, Coefficient and Conductivity Problems by the Methods with Bases Satisfying the Boundary Conditions Automatically. - Chein-Shan Liu; Lin Qiu (J. Sci. Comput., 2023)

Memory-Accelerating Methods for One-Step Iterative Schemes with Lie Symmetry Method Solving Nonlinear Boundary-Value Problem. - Chein-Shan Liu; Chih-Wen Chang; Chung-Lun Kuo (Symmetry, 2024)

A Symmetry of Boundary Functions Method for Solving the Backward Time-Fractional Diffusion Problems. - Chein-Shan Liu; Chung-Lun Kuo; Chih-Wen Chang (Symmetry, 2024)

Precise eigenvalues in the solutions of generalized Sturm-Liouville problems. - Chein-Shan Liu; Yung-Wei Chen; Chih-Wen Chang (Math. Comput. Simul., 2024)

Solving Least-Squares Problems via a Double-Optimal Algorithm and a Variant of the Karush-Kuhn-Tucker Equation for Over-Determined Systems. - Chein-Shan Liu; Chung-Lun Kuo; Chih-Wen Chang (Algorithms, 2024)

Re-Orthogonalized/Affine GMRES and Orthogonalized Maximal Projection Algorithm for Solving Linear Systems. - Chein-Shan Liu; Chih-Wen Chang; Chung-Lun Kuo (Algorithms, 2024)

The Trefftz methods for 3D biharmonic equation using directors and in-plane biharmonic functions. - Chein-Shan Liu; Chung-Lun Kuo (Eng. Comput., 2024)

Solving higher-order nonlocal boundary value problems with high precision by the fixed quasi Newton methods. - Chein-Shan Liu; Yung-Wei Chen; Jian-Hung Shen; Yen-Shen Chang (Math. Comput. Simul., 2025)