IIT Kharagpur Course , Prof. G.P. Raja Sekhar

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IIT Kharagpur Course , Prof. G.P. Raja Sekhar

Initial Value Problems (IVP) and existence theorem. Truncation error, deriving finite difference equations - Single step methods for I order IVP- Taylor series method, Euler method, Picards method of successive approximation - Runge Kutta Methods. Stability of single step methods - Multi step methods for I order IVP - Predictor-Corrector method, Euler PC method, Milne and Adams Moulton PC method - Stability of multi step methods, root condition - System of first order ODE, higher order IVPs - Linear Boundary Value Problems (BVP), finite difference methods, shooting methods, stability, error and convergence analysis - Non linear BVP, higher order BVP - Classification of PDEs, Finite difference approximations to partial derivatives - Solution of one dimensional heat conduction equation by Explicit and Implicit schemes (Schmidt and Crank Nicolson methods ), stability and convergence criteria - Laplace equation using standard five point formula and diagonal five point formula, Iterative methods for solving the linear systems - Hyperbolic equation, explicit / implicit schemes, method of characteristics. Solution of wave equation - Solution of I order Hyperbolic equation. Von Neumann stability

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Numerical methods of Ordinary and Partial Differential Equations by Prof. Dr. G.P. Raja Sekhar, Department of Mathematics, IITKharagpur. For more details on NPTEL visit httpnptel.iitm.ac.in

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- 1.Motivation with few Examples
- 2.Single - Step Methods for IVPs
- 3.Analysis of Single Step Methods
- 4.Runge - Kutta Methods for IVPs
- 5.Higher Order MethodsEquations
- 6.Error - Stability - Convergence of Single Step Methods
- 7.Tutorial - I
- 8.Tutorial - II
- 9.Multi-Step Methods (Explicit)
- 10.Multi-Step Methods (Implicit)
- 11.Convergence and Stability of multi step methods
- 12.General methods for absolute stability
- 13.Stability Analysis of Multi Step Method
- 14.Predictor - Corrector Methods
- 15.Mod-15 Lec 15 Some Comments on Multi - Step Methods
- 16.Finite Difference Methods - Linear BVPs
- 17.Mod-17 Lec 17 LinearNon - Linear Second Order BVPs
- 18.BVPS - Derivative Boundary Conditions
- 19.Higher Order BVPs
- 20.Shooting Method BVPs
- 21.Tutorial - III
- 22.Introduction to First Order PDE
- 23.Introduction to Second Order PDE
- 24.Finite Difference Approximations to Parabolic PDEs
- 25.Implicit Methods for Parabolic PDEs
- 26.Consistency, Stability and Convergence
- 27.Other Numerical Methods for Parabolic PDEs
- 28.Tutorial - IV
- 29.Matrix Stability Analysis of Finite Difference Scheme
- 30.Fourier Series Stability Analysis of Finite Difference Scheme
- 31.Finite Difference Approximations to Elliptic PDEs- I
- 32.Finite Difference Approximations to Elliptic PDEs - II
- 33.Finite Difference Approximations to Elliptic PDEs - III
- 34.Finite Difference Approximations to Elliptic PDEs - IV
- 35.Finite Difference Approximations to Hyperbolic PDEs - I
- 36.Finite Difference Approximations to Hyperbolic PDEs - II
- 37.Method of characteristics for Hyperbolic PDEs - I
- 38.Method of characterisitcs of Hyperbolic PDEs - II
- 39.Finite Difference Approximations to 1st order Hyperbolic PDEs
- 40.Summary, Appendices, Remarks

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