Preprints:

• Z. Sun, L. Ling, and M. Chen, Structure-preserving kernel-based methods for solving dissipative PDEs on surfaces (2023), arXiv:2312.17478
• M. Chen, L. Ling, and D. Yun, Proving the stability estimates of variational least-squares kernel-based methods (2023), arXiv:2312.07080
• W. Hu, Z. Fu, L. Ling, Simulating time-harmonic acoustic wave effects induced by periodic holes/inclusions on surfaces (2023), arXiv:2307.10009
  

Published Articles:

1. Realistic pattern formations on surfaces by adding arbitrary roughness.
   S. Li, L. Ling, S. Ruuth, and X. Wang,
   SIAM Journal on Applied Mathematics. Accepted 2024.
   
2. Enhancing RBF-FD efficiency for highly non-uniform nodes distributions via adaptivity.
   S. Li, L. Ling, X. Liu, P. K. Mishra, M. K. Sen, and J. Zhang.
   Numerical Mathematics: Theory, Methods and Applications. Online 2024. DOI: 10.4208/nmtma.OA-2023-0095
3. Exploring oversampling in RBF least-squares collocation method of lines for surface diffusion.
   M. Chen, and L. Ling.
   Numerical Algorithms. Online 2024. DOI: 10.1007/s11075-023-01741-4
4. A kernel-based least-squares collocation method for surface diffusion.
   M. Chen, K.C. Cheung, and L. Ling.
   SIAM Journal on Numerical Analysis. 61(3): 1386-1404, 2023.
5. A time-continuous embedding method for scalar hyperbolic conservation laws on manifolds.
   Y. Wang, B.-S. Wang, L. Ling, and W. S. Don.
   Journal of Scientific Computing, 93:84, 2022.
6. Solving interpolation problems on surfaces stochastically and greedily.
   M. Chen, L. Ling, and Y. Su.
   Dolomites Research Notes on Approximation, 15(3): 26-36, 2022.
7. Meshfree semi-Lagrangian methods for solving surface advection PDEs.
   A. Petras, L. Ling, and S. Ruuth.
   Journal of Scientific Computing, 93:11, 2022.
8. A kernel-based meshless conservative Galerkin method for solving Hamiltonian wave equations.
   Z.J. Sun, and L. Ling.
   SIAM Journal on Scientific Computing, 44(4): A2789--A2807, 2022.
9. A stochastic extended Rippa's algorithm for LpOCV.
   L. Ling, and F. Marchetti.
   Applied Mathematics Letters. 129:107955. 2022.
10. A localized extrinsic collocation method for Turing pattern formations on surfaces.
    Z. Tang, Z. Fu, M. Chen, and L. Ling.
    Applied Mathematics Letters. 122:107534. 2021
11. On variable and random shape Gaussian interpolations.
    S.N. Chiu, L. Ling and M. McCourt.
    Applied Mathematics and Computation. 377: 125159. 2020.
12. Complex pattern formations by spatial varying parameters.
    S. Li, and L. Ling.
    Advances in Applied Mathematics and Mechanics. 12(6): 1327-1352. 2020
    
13. Extrinsic meshless collocation methods for PDEs on manifolds.
    M. Chen and L. Ling.
    SIAM Journal on Numerical Analysis. 58(2): 988-1007. 2020
14. Kernel-based collocation methods for heat transport on evolving surfaces.
    M. Chen and L. Ling.
    Journal of Computational Physics. 405: 109166. 2020.
15. Solving Partial Differential Equations on Surfaces with Fundamental Solutions.
    M. Chen, K.C. Cheung, and L. Ling.  
    In: Alves C., Karageorghis A., Leitão V., Valtchev S. (eds) Advances in Trefftz Methods and Their Applications. SEMA SIMAI Springer Series, Springer, Cham. 23:1-11. 2020.
16. Meshfree seismic modeling using radial basis finite-difference with adaptive stencil size.
    X. Liu, P. K. Mishra, M.l K. Sen, and L. Ling.
    SEG Technical Program Expanded Abstracts : 2673-2677, 2020.
17. Meshless collocation methods for solving PDEs on surfaces.
    M. Chen, K.C. Cheung, and L. Ling.
    In A.H.-D. Cheng,  A. Tadeu (Eds.), WIT Transactions on Engineering Sciences, 126, 159-170, 2019.
18. Kernel-based meshless collocation methods for solving coupled bulk-surface PDEs.
    M. Chen and L. Ling.
    Journal of Scientific Computing. 81(1): 375-391. 2019.
19. Collocation methods for Cauchy problems of elliptic operators via conditional stabilities.
    S. Li and L. Ling.
    Communications in Computational Physics. 26(3): 785-808. 2019.
20. Weighted least-squares collocation methods for elliptic PDEs with mixed boundary conditions.
    S. Li and L. Ling.
    Engineering Analysis with Boundary Elements. 105: 146-154. 2019.
21. A stabilized radial basis-finite difference (RBF-FD) method with hybrid kernels.
    P. K. Mishra, G. E. Fasshauer, M .K. Sen and L. Ling.
    Computers and Mathematics with Applications. 77(9): 2354-2368. 2019.
22. Discrete least-squares radial basis functions approximations.
    S. Li, L. Ling and K.C. Cheung.
    Applied Mathematics and Computation.  355: 542-552. 2019.
23. A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces.
    A. Petras, L. Ling, C. Piret and S. Ruuth.
    Journal of Computational Physics. 381: 146-161. 2019.
24. An RBF-FD closest point method for solving PDEs on surfaces.
    A. Petras, L. Ling and S. Ruuth.
    Journal of Computational Physics. 370: 43-57. 2018.
25. Doubly stochastic radial basis function methods.
    F. L. Yang, L. Yan and L. Ling.
    Journal of Computational Physics. 363: 87-97. 2018.
26. Evaluation finite moment log-stable option pricing by a spectral method.
    X. Guo and L. Ling.
    Numerical Mathematics: Theory, Methods and Applications. 11(3): 437-452. 2018.
27. On meshfree numerical differentiation.
    L. Ling and Q. Ye.
    Analysis and Applications. 16(5): 717-739. 2018.
28. Fully adaptive kernel-based methods.
    L. Ling and S.N. Chiu.
    International Journal for Numerical Methods in Engineering. 114(4): 454-467. 2018.
29. A kernel-based embedding method and convergence analysis for surfaces PDEs.
    K.C. Cheung and L. Ling.
    SIAM Journal on Scientific Computing. 40(1), A266-A287. 2018.
30. H²-convergence of least-squares kernel collocation methods.
    K.C. Cheung, L. Ling and R. Schaback.
    SIAM Journal on Numerical Analysis. 56(1): 614-633. 2018.
    
31. Convergence studies for an adaptive meshless least-squares collocation method.
    K.C. Cheung and L. Ling.
    International Journal of Computational Methods and Experimental Measurements. 5(3): 377-386. 2017.
32. Meshless collocation methods with graph Laplacian for PDEs on folded surface.
    K.C. Cheung and L. Ling.
    Neural, Parallel, and Scientific Computations. 25: 79-90. 2017.
33. Numerical investigation on the effect of tumor on the thermal behavior inside the skin tissue.
    Z. J. Fu, Q. Xi, L. Ling and C.-Y. Cao.
    International Journal of Heat and Mass Transfer. 108, Part A, 1154–1163. 2017.
34. A fractional model for time-variant non-Newtonian flow.
    X. Yang, W. Chen, R. Xiao and L. Ling.
    Thermal Science. 21(1A): 61-68. 2017.
    
35. A fast block-greedy algorithm for quasi-optimal meshless trial subspace selection.
    L. Ling.
    SIAM Journal on Scientific Computing. 38(2): A1224–A1250. 2016.
36. Regularization for 2-D fractional sideways heat equations.
    C. Wang, L. Ling, X. Xiong and M. Li.
    Numerical Heat Transfer Fundamentals. 68(5):418–433. 2015
    
37. A localized meshless method for diffusion on folded surfaces.
    K.C. Cheung, L. Ling and S. Ruuth.
    Journal of Computational Physics. 297: 194–206. 2015
38. Method of approximate particular solutions for constant- and variable-order fractional diffusion models.
    Z.-J. Fu, W. Chen, and L. Ling.
    Engineering Analysis with Boundary Elements. 57: 37–46. 2015.
    
39. Numerical Caputo differentiation by radial basis functions.
    M. Li, Y. Wang, and L. Ling.
    Journal of Scientific Computing. 62(1):300–315. 2015.  
40. Collocation and optimization initialization.
    E. J. Kansa, and L. Ling.
    In A.H-D. Cheng, C. A. Brebbia (Eds.), WIT Transactions on Modelling and Simulation, 57, 55-62, 2014.
41. Solving moving-boundary problems with the wavelet adaptive radial basis functions method.
    L. Vrankar, N. A. Libre, L. Ling, G. Turk, and F. Runovc.
    Computers and Fluids.  86(5):37–44. 2013.
42. Convergent overdetermined-RBF-MLPG for solving second order elliptic PDEs.
    A. Shirzadi, and L. Ling.
    Advances in Applied Mathematics and Mechanics. 5(1):78–89. 2013.
    
43. Numerical simulations for space-time fractional diffusion equations.
    L. Ling, and M. Yamamoto.
    International Journal of Computational Methods. 10(2):1341001. 2013.   
44. Combinations of the method of fundamental solutions for general inverse source identification problems.
    F. Wand, W. Chen, and L. Ling.
    Applied Mathematics and Computation. 219(3):1173–1182. 2012.
45. Meshless simulations of the two-dimensional fractional-time convection-diffusion-reaction equations.
    A. Shirzadi, L. Ling, and S. Abbasbandy.
    Engineering Analysis with Boundary Elements. 36(11):1522–1527. 2012.
46. An adaptive-hybrid meshfree approximation method.
    L. Ling.
    International Journal for Numerical Methods in Engineering. 89(5):637-657. 2012
47. On numerical experiments for Cauchy problems of elliptic operators.
    F. L. Yang, and L. Ling.
    Engineering Analysis with Boundary Elements. 35(7):879–882. 2011.
48. Numerical methods for backward Markov chain driven Black-Scholes option pricing.
    C. Y. Au, S. L. Fung, and L. Ling.
    Frontiers of Mathematics in China. 6(1):17-33. 2011.
49. An energy regularization for Cauchy problems of Laplace equation in annulus domain.
    H. Han, L. Ling, and T. Takeuchi.
    Communications in Computational Physics. 9(4):878-896. 2011.
50. Approximate unconditional test procedure for comparing two ordered multinomials computational statistics and data analysis.
    M. L. Tang, W.-Y. Poon, L. Ling, Y. Liao, and H.-W. Chui.
    Computational Statistics and Data Analysis. 55(2): 955–963. 2011.
51. Optimality of the method of fundamental solutions.
    K. Y. Wong and L. Ling.
    Engineering Analysis with Boundary Elements. 35(1):42–46. 2011.
52. Adaptive-hybrid meshfree method.
    L. Ling.
    In Ch Zhang, M. H. Aliabadi, M. Schanz (Eds.), Advances in Boundary Element Techniques XI, page 252-257. ECltd, England, 2010.
53. Adaptive method of particular solution for solving 3D inhomogeneous elliptic equations.
    C. S. Chen, T. O. Kwok and L. Ling.
    International Journal of Computational Methods. 7(3):499-511. 2010.
54. An adaptive greedy technique for inverse boundary determination problem.
    F. L. Yang, L. Ling and T. Wei.
    Journal of Computational Physics. 229(22):8484–8496. 2010.
55. Dimension-splitting data points redistribution for meshless approximation.
    T. O. Kwok and L. Ling.
    Journal of Computational and Applied Mathematics. 235(3):736-746. 2010.
56. Moving-boundary problems solved by adaptive radial basis functions.
    L. Vrankar, E. J. Kansa, L. Ling, F. Runovc and G. Turk.
    Computers and Fluids. 39(9):1480-1490. 2010.
57. Numerical simulations of 2D fractional subdiffusion problems.
    H. Brunner, L. Ling and M. Yamamoto.
    Journal of Computational Physics. 229(18):6613-6622. 2010
58. Confidence intervals for a difference between proportions based on paired data.
    M. L. Tang, M. H. Ling, L. Ling and G. L. Tian.
    Statistics in Medicine. 29(1): 86-96. 2010.
59. Effective condition number for boundary knot method.
    F. Z. Wang, L. Ling and W. Chen.
    Computers, Materials & Continua. 12(1):57-70. 2009.
60. An improved subspace selection algorithm for meshless collocation methods.
    L. Ling and R. Schaback.
    International Journal for Numerical Methods in Engineering. 80(13):1623-1639. 2009.
    
61. On convergence of a least-squares Kansa's method for the modified Helmholtz equations.
    T. O. Kwok and L. Ling.
    Advances in Applied Mathematics and Mechanics. 1(3):367-382. 2009.
62. Numerical simulation of two-dimensional combustion using mesh-free methods.
    E. J. Kansa, R. C. Aldredge and L. Ling.
    Engineering Analysis with Boundary Elements. 33(7):940-950. 2009.
63. Point sources identification problems for heat equations.
    L. Ling, and T. Takeuchi.
    Communications in Computational Physics. 5(5):897-913. 2009.
64. On convergent numerical algorithms for unsymmetric collocation.
    C.-F. Lee, L. Ling and R. Schaback.
    Advances in Computational Mathematics. 30(4):339-354. 2009.
65. Applicability of the method of fundamental solutions.
    T. W. Drombosky, A. L. Meyer and L. Ling.
    Engineering Analysis with Boundary Elements. 33(5): 637-643. 2009.
66. Boundary control for inverse Cauchy problems of the Laplace equations.
    L. Ling, and T. Takeuchi.
    Computer Modeling in Engineering & Sciences. 29(1):45-54. 2008.
67. Stable and convergent unsymmetric meshless collocation methods.
    L. Ling and R. Schaback.
    SIAM Journal on Numerical Analysis. 46(3):1097-1115. 2008.
68. Arbitrary precision compuations of Kansa's method.
    L. Ling.
    In A. Ferreira, E. J. Kansa, G. Fasshauer, V. Leitão (Eds.), Progress on meshless methods, 11, 77-83, Springer, New York, 2008.
69. Stability analysis for the penalty plus hybrid and the direct Trefftz methods for singularity problems.
    Z. C. Li, H. T. Huang, J. Huang and L. Ling.
    Engineering Analysis with Boundary Elements. 31(2):163-175. 2007.
70. Method of fundamental solutions with regularization techniques for Cauchy problems of elliptic operators.
    T. Wei, Y. C. Hon and L. Ling.
    Engineering Analysis with Boundary Elements. 31(4): 373-385. 2007.
71. An accurate refinement scheme for inverse heat source location identifications.
    L. Ling, and T. Takeuchi.
    Computer Modeling in Engineering & Sciences. 20(2): 99-110. 2007.
72. A computational method for solving Cauchy problems of elliptic operators.
    Y. C. Hon, T. Wei, and L. Ling.
    In G. R. Liu, V. B. C. Tan, and X. Han (Eds), Computational methods, 1375–1384. Springer, New York, 2006.
73. Identification of source locations in two-dimensional heat equations.
    L. Ling, Y. C. Hon, M. Yamamoto and T. Takeuchi.
    Inverse Problems. 22(4):1289-1305. 2006.
74. Finding numerical derivatives for unstructured and noisy data by multiscale kernels.
    L. Ling.
    SIAM Journal on Numerical Analysis. 44(4): 1780-1800. 2006.
75. Adaptive multiquadric collocation for boundary layer problems.
    L. Ling and M. R. Trummer.
    Computational and Applied Mathematics. 188(2):265-282. 2006.
76. Results on meshless collocation techniques.
    L. Ling, R. Opfer and R. Schaback.
    Engineering Analysis with Boundary Elements.30(4): 247-253. 2006.
77. The role of the multiquadric shape parameters in solving elliptic partial differential equations.
    J. Wertz, E. J. Kansa and L. Ling.
    Computers and Mathematics with Applications. 51(8):1335-1348. 2006.
78. Inverse source identification for Poisson equation.
    L. Ling, Y. C. Hon and M. Yamamoto.
    Inverse Problems in Science and Engineering. 13(4):433-447. 2005.
79. On approximate cardinal preconditioning methods for solving PDEs with radial basis functions.
    D. Brown, L. Ling, E. J. Kansa and J. Levesley.
    Engineering Analysis with Boundary Elements. 29(4):343-353. 2005.
80. Numerical analysis of parameters in a laminated beam model by radial basis functions.
    Y. C. Hon, L. Ling and K. M. Liew.
    Computers, Materials & Continua. 2(1):39-50. 2005.
81. A least squares preconditioner for radial basis functions collocation methods.
    L. Ling and E. J. Kansa.
    Advances in Computational Mathematics. 23(1-2):31-54. 2005.
82. Multivariate quasi-interpolation formula with dimension-splitting multiquadric basis.
    L. Ling.
    Applied Mathematics and Computation. 161(1):195-209. 2005.
83. Improved numerical solver for Kansa's method based on affine space decomposition.
    L. Ling and Y. C. Hon.
    Engineering Analysis with Boundary Elements. 29(12):1077-1085. 2005.
84. Multiquadric collocation method with integral formulation for boundary layer problems.
    L. Ling and M. R. Trummer.
    Computers and Mathematics with Applications. 48(5-6):927-941. 2004.
85. A univariate quasi multiquadric interpolation with better smoothness.
    L. Ling.
    Computers and Mathematics with Applications. 48(5-6):897-912. 2004.
86. Preconditioning for radial basis functions with domain decomposition methods.
    L. Ling and E. J. Kansa.
    Mathematical and Computer Modelling. 40(13):1413-1427. 2004.
87. A volumetric integral radial basis function method for time dependent partial differential equations.
    E. J. Kansa, H. Power, G. E. Fasshauer and L. Ling.
    Engineering Analysis with Boundary Elements. 28(10):1191-1206. 2004.

Edited Special Issues:

1. Advanced Mesh-based and Particle-based Numerical Methods for Engineering and Applied Mathematics Problems.
   C.-T. Wu, L. Wang, B. Bonello, L. Ling, N. Ma, M. A. Schweitzer (Eds.), Mathematical Problems in Engineering, Hindawi, 2017
2. Special Issue on Inverse Problems and Applications.
   M. Yamamoto, J. Cheng, Y. C. Hon, J.-Y. Lee, L. Ling, G.-R. Liu, J. Wang (Eds.), Applicable Analysis, 91(4), 2012.
3. Proceeding of the International Conference on Inverse Problems 2010.
   Y. C. Hon and L. Ling (Eds), Journal of Physics: Conference Series, Vol. 290, 2011.
4. Numerical methods and analysis for PDEs and inverse problems.
   C. S. Chen, M.-C. Lai, L. Ling, J. Li, M. Yamamoto (Eds.), Advances in Applied Mathematics and Mechanics, 1(6). 2009.

Textbooks:

1. Mathematics of Fairness.
   S. N. Chiu, and L. Ling.
   Series: Hong Kong Mathematical Society Texts in General Education, Vol. 1, Pearson Education Asia, 2012.
2. Manage Your Money without Formulas.
   L. Ling.
   Series: Hong Kong Mathematical Society Texts in General Education, Vol. 2, Pearson Education Asia, 2012.
3. Discovering Hong Kong by SPSS.
   H. W. Chiu, and L. Ling.
   Series: Hong Kong Mathematical Society Texts in General Education, Vol. 3, Pearson Education Asia, 2012.
4. Estimating the World.
   W. S. Don, and L. Ling.
   Series: Hong Kong Mathematical Society Texts in General Education, Vol. 4, Pearson Education Asia, 2012.
5. Smart Decisions.
   W. C. Shiu, and L. Ling.
   Series: Hong Kong Mathematical Society Texts in General Education, Vol. 8, Pearson Education Asia, 2012.