An efficient B-spline difference method for solving system of nonlinear parabolic PDEs

Keywords

Mathematics, Collocation method, Partial differential equation, Parabolic partial differential equation, Nonlinear system

References

• New Exact Solutions of One Nonlinear Equation in Mathematical Biology and Their PropertiesRoman Cherniha — 2001
• Restrictive Taylor's approximation for solving convection-diffusion equationHassan N.A. Ismail — 2004
• The numerical solution of nonlinear high dimensional generalized Benjamin-Bona-Mahony-Burgers equation via the meshless method of radial basis functionsMehdi Dehghan, Mostafa Abbaszadeh, Akbar Mohebbi — 2014
• Spline Collocation Differentiation MatricesRobert D. Russell, Weiwei Sun — 1997
• Cubic spline difference method for heat conductionChi-Chang Wang, Jin-Hung Huang, Dane-Jong Yang — 2012
• An implicit high accuracy variable mesh scheme for 1-D non-linear singular parabolic partial differential equationsR. K. Mohanty — 2007
• Fifth-degree B-spline solution for a fourth-order parabolic partial differential equationsHikmet Çağlar, Nazan Çağlar — 2008
• A Trust Region Algorithm for Nonlinearly Constrained OptimizationRichard H. Byrd, Robert B. Schnabel, Gerald A. Shultz — 1987
• B-splines methods with redefined basis functions for solving fourth order parabolic partial differential equationsR.C. Mittal, Reema Jain — 2011
• Exact and numerical solutions of the generalized fisher equationRoman Cherniha, V. A. Dutka — 2001
• Convergence of O ( h 4 ) cubic spline collocation methods for elliptic partial differential equationsElias N. Houstis, E. A. Vavalis, J. R. Rice — 1988
• Collocation method using quartic B-spline for the equal width (EW) equationK. R. Raslan — 2005
• The theory of splines and their applicationsH. O. K, J. H. Ahlberg, E. N. Nilson — 1969
• Fitted mesh B-spline collocation method for singularly perturbed differential-difference equations with small delayMohan K. Kadalbajoo, Devendra Kumar — 2008
• A linearly semi-implicit compact scheme for the Burgers–Huxley equationShenggao Zhou, Xiaoliang Cheng — 2011
• A Higher Order Numerical Scheme for Some Nonlinear Differential Equations: Models in BiologyR.C. Mittal, Ram Jiwari — 2011
• High-Order Compact Difference Scheme for Convection-Diffusion Problems on Nonuniform GridsX. Wang, Z.F. Yang, Guohe Huang — 2005
• Redefined cubic B-splines collocation method for solving convection–diffusion equationsR.C. Mittal, Reema Jain — 2012
• An implicit RBF meshless approach for time fractional diffusion equationsQ. Liu, Yuantong Gu, Peixian Zhuang — 2011
• Principles of mathematical analysisWalter Rudin — 1964

Cited by

• Biological treatment of slaughterhouse wastewater: kinetic modeling and prediction of effluentMoein Besharati Fard, Seyed Ahmad Mirbagheri, Alireza Pendashteh — 2019
• A Comparative Study of Explicit and Stable Time Integration Schemes for Heat Conduction in an Insulated WallHumam Kareem Jalghaf, Issa Omle, Endre Kovács — 2022
• New Analytical Results and Comparison of 14 Numerical Schemes for the Diffusion Equation with Space-Dependent Diffusion CoefficientMahmoud Saleh, Endre Kovács, Imre Ferenc Barna — 2022
• Comparison of Old and New Stable Explicit Methods for Heat Conduction, Convection, and Radiation in an Insulated Wall with Thermal BridgingHumam Kareem Jalghaf, Endre Kovács, Betti Bolló — 2022
• Orthogonal cubic splines for the numerical solution of nonlinear parabolic partial differential equationsJavad Alavi, Hossein Aminikhah — 2023
• Explicit Stable Finite Difference Methods for Diffusion-Reaction Type EquationsHumam Kareem Jalghaf, Endre Kovács, János Majár — 2021

Related papers

• A comparative study of collocation methods for the numerical solution of differential equations.Margaret Modupe. Kajotoni — 2008
• A Wavelet Collocation Method of Nonlinear Partial Differential Equation Based on EnergyHuaiping Yan — 2008
• Transient Flow in Unsaturated Porous MediaSheng H. Lin — 1978
• A comparison of Galerkin, collocation and the method of lines for partial differential equationsTim Hopkins, R. Wait — 1978
• The Collocation Method in the Numerical Solution of Boundary Value Problems for Neutral Functional Differential Equations. Part II: Differential Equations with Deviating ArgumentsStefano Maset — 2015
• Spectral Collocation Method for Parabolic Partial Differential Equations with Neumann Boundary ConditionsMohammad Javidi, A. Golbabai — 2007
• Pseudospectral method and Darvishi's preconditioning for solving system of time dependent partial differential equationsMohammad Masoud Javidi — 2006
• Stable Two-Step Runge-Kutta Collocation Methods for Oscillatory Systems of Initial Value Problems in ODEsDauda Gulibur Yakubu, A. G. Madaki, A. M. Kwami — 2013
• Solving General Second Order Ordinary Differential Equations by a One- Step Hybrid Collocation MethodT. A. Anake, D. O. Awoyemi, Adetola A. Adesanya — 2012