TY - BOOK AU - Gorman, D. J. PY - 1975 DA - 1975// TI - Free Vibrations Analysis of Beams and Shafts PB - Wiley CY - New York ID - Gorman1975 ER - TY - BOOK AU - Meirovitch, L. PY - 1997 DA - 1997// TI - Principles and Techniques of Vibrations PB - Prentice Hall CY - New Jersey ID - Meirovitch1997 ER - TY - BOOK AU - Debnath, L. PY - 1997 DA - 1997// TI - Nonlinear Partial Differential Equations for Scientists and Engineers PB - Birkhauser CY - Boston UR - https://doi.org/10.1007/978-1-4899-2846-7 DO - 10.1007/978-1-4899-2846-7 ID - Debnath1997 ER - TY - JOUR AU - Hereman, W. AU - Banerjee, P. P. AU - Korpel, A. AU - Assanto, G. PY - 1986 DA - 1986// TI - Exact solitary wave solutions of non-linear evolution and wave equations using a direct algebraic method JO - J. Phys. A, Math. Gen. VL - 19 UR - https://doi.org/10.1088/0305-4470/19/5/016 DO - 10.1088/0305-4470/19/5/016 ID - Hereman1986 ER - TY - JOUR AU - Xu, Z. H. AU - Xian, D. Q. AU - Chen, H. L. PY - 2010 DA - 2010// TI - New periodic solitary-wave solutions for the Benjamin-Ono equation JO - Appl. Math. Comput. VL - 215 ID - Xu2010 ER - TY - JOUR AU - Soh, C. W. PY - 2008 DA - 2008// TI - Euler-Bernoulli beams from a symmetry standpoint-characterization of equivalent equations JO - J. Math. Anal. Appl. VL - 345 UR - https://doi.org/10.1016/j.jmaa.2008.04.023 DO - 10.1016/j.jmaa.2008.04.023 ID - Soh2008 ER - TY - JOUR AU - Lai, H. AU - Ma, C. PY - 2010 DA - 2010// TI - The lattice Boltzmann model for the second-order Benjamin-Ono equations JO - J. Stat. Mech. VL - 2010 ID - Lai2010 ER - TY - JOUR AU - Bratsos, A. G. PY - 1998 DA - 1998// TI - The solution of the Boussinesq equation using the method of lines JO - Comput. Methods Appl. Mech. Eng. VL - 157 UR - https://doi.org/10.1016/S0045-7825(97)00211-9 DO - 10.1016/S0045-7825(97)00211-9 ID - Bratsos1998 ER - TY - JOUR AU - Ismail, M. S. AU - Bratsos, A. G. PY - 2003 DA - 2003// TI - A predictor-corrector scheme for the numerical solution of the Boussinesq equation JO - J. Appl. Math. Comput. VL - 13 UR - https://doi.org/10.1007/BF02936071 DO - 10.1007/BF02936071 ID - Ismail2003 ER - TY - JOUR AU - Dehghan, M. AU - Salehi, R. PY - 2012 DA - 2012// TI - A meshless based numerical technique for traveling solitary wave solution of Boussinesq equation JO - Appl. Math. Model. VL - 36 UR - https://doi.org/10.1016/j.apm.2011.07.075 DO - 10.1016/j.apm.2011.07.075 ID - Dehghan2012 ER - TY - JOUR AU - Mohanty, R. K. AU - Kaur, D. PY - 2016 DA - 2016// TI - High accuracy implicit variable mesh methods for numerical study of special types of fourth order non-linear parabolic equations JO - Appl. Math. Comput. VL - 273 ID - Mohanty2016 ER - TY - JOUR AU - Jain, M. K. AU - Jain, R. K. AU - Mohanty, R. K. PY - 1990 DA - 1990// TI - A fourth order difference method for the one-dimensional general quasilinear parabolic partial differential equation JO - Numer. Methods Partial Differ. Equ. VL - 6 UR - https://doi.org/10.1002/num.1690060403 DO - 10.1002/num.1690060403 ID - Jain1990 ER - TY - JOUR AU - Mohanty, R. K. AU - Jain, M. K. AU - Kumar, D. PY - 2000 DA - 2000// TI - Single cell finite difference approximations of O(kh2+h4)$O(kh^{2}+h^{4})$ for ∂u/∂x$\partial u/\partial x$ for one space dimensional nonlinear parabolic equation JO - Numer. Methods Partial Differ. Equ. VL - 16 UR - https://doi.org/3.0.CO;2-J DO - 3.0.CO;2-J ID - Mohanty2000 ER - TY - JOUR AU - Mohanty, R. K. AU - Karaa, S. AU - Arora, U. PY - 2007 DA - 2007// TI - An O(k2+kh2+h4)$O(k^{2}+kh^{2}+h^{4})$ arithmetic average discretization for the solution of 1-D nonlinear parabolic equations JO - Numer. Methods Partial Differ. Equ. VL - 23 UR - https://doi.org/10.1002/num.20195 DO - 10.1002/num.20195 ID - Mohanty2007 ER - TY - JOUR AU - Mohanty, R. K. PY - 2007 DA - 2007// TI - An implicit high accuracy variable mesh scheme for 1-D non-linear singular parabolic partial differential equations JO - Appl. Math. Comput. VL - 186 ID - Mohanty2007 ER - TY - JOUR AU - Mohanty, R. K. AU - Kumar, R. PY - 2014 DA - 2014// TI - A new fast algorithm based on half-step discretization for one space dimensional quasilinear hyperbolic equations JO - Appl. Math. Comput. VL - 244 ID - Mohanty2014 ER - TY - JOUR AU - Mohanty, R. K. AU - Gopal, V. PY - 2014 DA - 2014// TI - High accuracy non-polynomial spline in compression method for one-space dimensional quasi-linear hyperbolic equations with significant first order space derivative term JO - Appl. Math. Comput. VL - 238 ID - Mohanty2014 ER - TY - JOUR AU - Mohanty, R. K. AU - Jha, N. AU - Kumar, R. PY - 2015 DA - 2015// TI - A new variable mesh method based on non-polynomial spline in compression approximations for 1D quasilinear hyperbolic equations JO - Adv. Differ. Equ. VL - 2015 UR - https://doi.org/10.1186/s13662-015-0672-7 DO - 10.1186/s13662-015-0672-7 ID - Mohanty2015 ER - TY - JOUR AU - Talwar, J. AU - Mohanty, R. K. AU - Singh, S. PY - 2015 DA - 2015// TI - A new spline in compression approximation for one space dimensional quasilinear parabolic equations on a variable mesh JO - Appl. Math. Comput. VL - 260 ID - Talwar2015 ER - TY - JOUR AU - Talwar, J. AU - Mohanty, R. K. AU - Singh, S. PY - 2016 DA - 2016// TI - A new algorithm based on spline in tension approximation for 1D quasi-linear parabolic equations on a variable mesh JO - Int. J. Comput. Math. VL - 93 UR - https://doi.org/10.1080/00207160.2015.1074682 DO - 10.1080/00207160.2015.1074682 ID - Talwar2016 ER - TY - JOUR AU - Siraj-ul-Islam AU - Vertnik, R. AU - Šarlen, B. PY - 2013 DA - 2013// TI - Local radial basis function collocation method along with explicit time stepping for hyperbolic partial differential equations JO - Appl. Numer. Math. VL - 67 UR - https://doi.org/10.1016/j.apnum.2011.08.009 DO - 10.1016/j.apnum.2011.08.009 ID - Siraj-ul-Islam2013 ER - TY - JOUR AU - Mohanty, R. K. AU - Kaur, D. PY - 2016 DA - 2016// TI - Numerov type variable mesh approximations for 1D unsteady quasi-linear biharmonic problem: application to Kuramoto-Sivashinsky equation JO - Numer. Algorithms ID - Mohanty2016 ER - TY - JOUR AU - Conte, S. D. PY - 1957 DA - 1957// TI - A stable implicit finite difference approximation to a fourth order parabolic equation JO - J. Assoc. Comput. Mech. VL - 4 UR - https://doi.org/10.1145/320856.320861 DO - 10.1145/320856.320861 ID - Conte1957 ER - TY - JOUR AU - Crandall, S. H. PY - 1957 DA - 1957// TI - Optimum recurrence formulas for a fourth order parabolic partial differential equation JO - J. Assoc. Comput. Mach. VL - 4 UR - https://doi.org/10.1145/320893.320902 DO - 10.1145/320893.320902 ID - Crandall1957 ER - TY - JOUR AU - Evans, D. J. PY - 1965 DA - 1965// TI - A stable explicit method for the finite difference solution of a fourth order parabolic partial differential equation JO - Comput. J. VL - 8 UR - https://doi.org/10.1093/comjnl/8.3.280 DO - 10.1093/comjnl/8.3.280 ID - Evans1965 ER - TY - JOUR AU - Fairweather, G. AU - Gourley, A. R. PY - 1967 DA - 1967// TI - Some stable difference approximations to a fourth order parabolic partial differential equation JO - Math. Comput. VL - 21 UR - https://doi.org/10.1090/S0025-5718-1967-0221785-2 DO - 10.1090/S0025-5718-1967-0221785-2 ID - Fairweather1967 ER - TY - CHAP AU - Collatz, L. ED - Miller, J. J. H. PY - 1973 DA - 1973// TI - Hermitian methods for initial value problems in partial differential equations BT - Topics in Numerical Analysis PB - Academic Press CY - New York ID - Collatz1973 ER - TY - JOUR AU - Andrade, C. AU - McKee, S. PY - 1977 DA - 1977// TI - High accuracy A.D.I methods for fourth-order parabolic equations with variable coefficients JO - J. Comput. Appl. Math. VL - 3 UR - https://doi.org/10.1016/0771-050X(77)90019-5 DO - 10.1016/0771-050X(77)90019-5 ID - Andrade1977 ER - TY - JOUR AU - Twizell, E. H. AU - Khaliq, A. Q. M. PY - 1983 DA - 1983// TI - A difference scheme with high accuracy in time for fourth order parabolic equations JO - Comput. Methods Appl. Mech. Eng. VL - 41 UR - https://doi.org/10.1016/0045-7825(83)90054-3 DO - 10.1016/0045-7825(83)90054-3 ID - Twizell1983 ER - TY - JOUR AU - Evans, D. J. AU - Yousif, W. S. PY - 1991 DA - 1991// TI - A note on solving the fourth-order parabolic equation by the AGE method JO - Int. J. Comput. Math. VL - 40 UR - https://doi.org/10.1080/00207169108804004 DO - 10.1080/00207169108804004 ID - Evans1991 ER - TY - JOUR AU - Khan, A. AU - Khan, I. AU - Aziz, T. PY - 2005 DA - 2005// TI - Sextic spline solution for solving a fourth-order parabolic partial differential equation JO - Int. J. Comput. Math. VL - 82 UR - https://doi.org/10.1080/00207160512331331165 DO - 10.1080/00207160512331331165 ID - Khan2005 ER - TY - JOUR AU - Caglar, H. AU - Caglar, N. PY - 2008 DA - 2008// TI - Fifth-degree B-spline solution for a fourth-order parabolic partial differential equations JO - Appl. Math. Comput. VL - 201 ID - Caglar2008 ER - TY - JOUR AU - Rashidinia, J. AU - Mohammadi, R. PY - 2010 DA - 2010// TI - Sextic spline solution of variable coefficient fourth-order parabolic equations JO - Int. J. Comput. Math. VL - 87 UR - https://doi.org/10.1080/00207160903085820 DO - 10.1080/00207160903085820 ID - Rashidinia2010 ER - TY - JOUR AU - Mittal, R. C. AU - Jain, R. K. PY - 2011 DA - 2011// TI - B-splines methods with redefined basis functions for solving fourth order parabolic partial differential equations JO - Appl. Math. Comput. VL - 217 ID - Mittal2011 ER - TY - JOUR AU - Mohammadi, R. PY - 2014 DA - 2014// TI - Sextic B-spline collocation method for solving Euler-Bernoulli beam models JO - Appl. Math. Comput. VL - 241 ID - Mohammadi2014 ER - TY - JOUR AU - Siddiqi, S. S. AU - Arshed, S. PY - 2014 DA - 2014// TI - Quintic B-spline for the numerical solution of the good Boussinesq equation JO - J. Egypt. Math. Soc. VL - 22 UR - https://doi.org/10.1016/j.joems.2013.06.015 DO - 10.1016/j.joems.2013.06.015 ID - Siddiqi2014 ER - TY - JOUR AU - Mohanty, R. K. AU - Evans, D. J. PY - 2003 DA - 2003// TI - The numerical solution of fourth order mildly qausi-linear parabolic initial boundary value problem of second kind JO - Int. J. Comput. Math. VL - 80 UR - https://doi.org/10.1080/0020716031000148476 DO - 10.1080/0020716031000148476 ID - Mohanty2003 ER - TY - BOOK AU - Kelly, C. T. PY - 1995 DA - 1995// TI - Iterative Methods for Linear and Non-linear Equations PB - SIAM CY - Philadelphia UR - https://doi.org/10.1137/1.9781611970944 DO - 10.1137/1.9781611970944 ID - Kelly1995 ER - TY - BOOK AU - Varga, R. S. PY - 2000 DA - 2000// TI - Matrix Iterative Analysis PB - Springer CY - New York UR - https://doi.org/10.1007/978-3-642-05156-2 DO - 10.1007/978-3-642-05156-2 ID - Varga2000 ER - TY - JOUR AU - Fu, Z. AU - Liu, S. AU - Liu, S. D. AU - Zhao, Q. PY - 2003 DA - 2003// TI - The JEFE method and periodic solutions of two kinds of nonlinear wave equations JO - Commun. Nonlinear Sci. Numer. Simul. VL - 8 UR - https://doi.org/10.1016/S1007-5704(02)00082-5 DO - 10.1016/S1007-5704(02)00082-5 ID - Fu2003 ER -