1 Dept. of Mathematics Indian Institute of Technology Delhi Hauz Khas, New Delhi , India Tel. (O): (91)-(11) Fax: (91)-(11) s: Webpage: mmehra D.O.B.: August , Female Languages Known: English, Hindi Marital Status: Married Professional Experiences (Feb Continuing) Associate Professor in Department of Mathematics, Indian institute of Technology Delhi, India. (Jan Jan. 2015) Assistant Professor in Department of Mathematics, Indian institute of Technology Delhi, India. Organized workshop on inverse problems and wavelets with applications to real world systems in Aug as a coordinator List of courses taught at IIT Delhi MAL630 (Partial Differential Equations). MAL524 (Numerical Analysis), Webpage: mmehra/mal524/math.html. MAL120 (Mathematics-II), Webpage: rksharma/mal120/main.html. MAL373 (Wavelet and Applications), Webpage: mmehra/mal373/math.html. MAL110 (Mathematics-I), Webpage: rksharma/mal110/main.html. MAL519 (Introduction to computers and programming). MAL518 (Methods of Applied Mathematics). MAL335 (Differential Equations: Theory and Numerical methods). MAL355 (Partial Differential Equations: Theory and Computation). (May-July 2013) Visiting professor position at University of Bremen, Bremen, Germany (July 2012) Visiting position at University of Bremen, Bremen, Germany (May 2008-July 2008) Visiting position at ENS, Paris, France
2 (July ) Postdoc Fellow with Nicholas Kevlahan in Department of Mathematics & Statistics, McMaster University, Canada. List of courses taught at McMaster Univ. Math 2A03 (Calculus III), Spring/Summer 2007, Webpage: mmehra/math2a03/math.html. Math 3FF3 (Partial Differential Equations), Winter 2007, Webpage: mmehra/math3ff3/math.html. Math 3D03(Some part of Mathematical Physics II(Confomal Mapping and Probability Theory)), Winter Math 4Q03/6Q03(Numerical Methods for Ordinary and Partial Differential Equations), Winter 2006, Webpage:http://web.iitd.ac.in/ mmehra/math4q03/math.html. Math 2E03 (Introduction to Modelling), Fall 2005, Webpage: mmehra/math2e03/m2e3.html. (Jan May 2005) Teaching Assistant in Department of Mathematics & statistics, Indian Institute of Technology (IIT) Kanpur, India. Tutor in the core course Math 203 (Differential Equations) of undergraduate students (July Dec. 2004) at IIT Kanpur, India. Honors Research interests Ph.D Students Outstanding young faculty fellowship from IIT Delhi Member in the Editorial board Journal of Wavelet Theory and Applications International Journal of BioSciences and Technology Reviewing job for for some selected journals Journal of Computational Physics Journal of Computational and Applied Mathematics Communication in Numerical methods in Engineering South East Asian Journal of Mathematics and Mathematical Sciences Applied Mathematics and Computation Applications of Wavelets in Partial Differential Equations and Numerical Analysis Ratikanta Behera (Completed), Postdoc in University of Notre Dame, USA. Kavita Goyal (Completed), Postdoc in University of Liege, Belgium. Kuldip Singh Patel (in progress) An adaptive meshfree diffusion wavelet method for partial differential equation Representative Publications on the sphere (with Kavita Goyal), Journal of Computational Physics, Vol. 272 (2014) pp
3 Publications A suit on wavelet differentiation algorithms(with Kavita Goyal), ACM Transaction on Mathematical software, Vol. 39 (4) (2013). An Adaptive wavelet collocation method for partial differential equations on the sphere (with Nicholas Kevlahan), Journal of Computational Physics, Vol. 227 (2008) pp An adaptive multilevel wavelet solver for elliptic equations on an optimal spherical geodesic grid (with Nicholas Kevlahan), SIAM Journal of Scientific Computing, Vol. 30 (6) (2008) pp Time accurate Fast Wavelet-Taylor Galerkin method for partial differential equations(with B. V. Rathish Kumar), Numerical methods for partial differential equations, Vol. 22 (2) (2005) pp Wavelet Taylor Galerkin method for Burgers equation (with B. V. Rathish Kumar), BIT Numerical Mathematics, Vol. 45 (3) (2005) pp Time-Accurate solution of Advection-Diffusion problems by Wavelet Taylor Galerkin method(with B. V. Rathish Kumar), Communications in Numerical Methods in Engineering, Vol. 21 (2005) pp A Time-Accurate pseudo-wavelet scheme for Parabolic and Hyperbolic PDE s (with B. V. Rathish Kumar), Nonlinear Analysis, Vol. 63 (2005) pp. e345- e356. A dynamic adaptive wavelet method for solution of the Schrodinger equation (withratikantabehera),to appear in Journal of Multiscale Modelling. Multilevel approximation of the gradient operator on an adaptive spherical geodesic grid (with Ratikanta Behera and Nicholas Kevlahan), to appear in Advances in Computational Mathematics, DOI /s z, A Fast Adaptive Diffusion Wavelet Method for Burger s equation (with Kavita Goyal), Computers and Mathematics with Applications, Vol. 68(2014) pp Solution of differential-difference equations arising from mathematical model of granulocytopoiesis (with Ranjan K. Mallik), Differential equations and Dynamical systems, Vol. 22 (1) (2014) pp Applications and properties of different kinds of wavelets (with Ratikanta Behera), Indian Journal of Industrial and Applied Mathematics, Vol. 4 (1) (2013) pp Integration of barotropic vorticity equation over spherical geodesic grid using multilevel adaptive wavelet collocation method(with Ratikanta Behera), Applied Mathematical Modelling, Vol. 37 (2013) pp Approximate solution of modified Camassa-Holm and modified Degasperis-Procesi (mdp) equations using wavelet optimized finite difference method(with Ratikanta Behera) International Journal of Wavelets, Multiresolution and Information Processing, Vol. 11 (2) (2013). Wavelet optimized finite difference method using interpolating wavelets for selfadjoint singularly perturbed problems(with Vivek Kumar), Journal of Computational and Applied Mathematics, Vol. 230 (2009) pp
4 Error Estimates for linear PDEs solved by wavelet based Taylor-Galerkin Schemes (With B. V. Rathish Kumar), International Journal of Wavelets, Multiresolution and Information Processing, Vol. 7 (2009) pp Wavelet optimized finite difference using interpolating wavelets for solving singularly perturbed problems (with Vivek Kumar), Journal of Wavelet Theory and Applications, Vol. 1 (1) (2007) pp Fast Wavelet-Taylor Galerkin method for linear and nonlinear waves problems (with Vivek Kumar), Applied Mathematics and Computation, Vol. 189 (2) (2007) pp Error Estimates for time accurate wavelet based schemes for hyperbolic PDE s (with B. V. Rathish Kumar), International Journal of Wavelets, Multiresolution and Information Processing, Vol. 5 (4) (2007) pp Cubic spline adaptive wavelet scheme to solve singularly perturbed reaction diffusion problems (with Vivek Kumar), International Journal of Wavelets, Multiresolution and Information Processing, Vol. 5 (2) (2007) pp Time accurate fast three-step wavelet Galerkin method for PDE s (with B. V. Rathish Kumar), International Journal of Wavelets, Multiresolution and Information Processing, Vol. 4 (1) (2006) pp A three-step Wavelet Galerkin method for Parabolic and Hyperbolic PDE s(with B. V. Rathish Kumar), International Journal of computer Mathematics, Vol. 83(1) (2006) pp Time-accurate solutions of Korteweg-de Vries equation using Wavelet Galerkin Method(with B. V. Rathish Kumar), Applied Mathematics and Computation, Vol. 162 (2005) pp A time-accurate pseudo-wavelet scheme for two-dimensional turbulence (with B. V. Rathish Kumar), International Journal of Wavelets, Multiresolution and Information Processing, Vol. 3(4) (2005) pp Wavelet Multilayer Taylor Galerkin schemes for Hyperbolic and Parabolic problems (with B. V. Rathish Kumar), Applied Mathematics and Computation, Vol. 166 (2005) pp A Wavelet-Taylor Galerkin method for Parabolic and Hyperbolic PDE s(with B. V. Rathish Kumar), International Journal of computational methods, Vol. 2 (1) (2005) pp Wavelet based preconditioners for sparse linear systems (with B. V. Rathish Kumar), Applied Mathematics and Computation,Vol. 171 (2005) pp Non stationary iterative solvers on PC cluster (with B. V. Rathish Kumar and Shalini), Advances in Engineering Software, Vol. 36 (2005) pp Krylov Subspace solvers in parallel numerical computations of partial differential equations modelling heat transfer applications (with B. V. Rathish Kumar, Bipin Kumar, Shalini, Mani Mehra, Peeyush Chandra, and V. Raghvendra),
5 International Journal of Numerical Heat Transfer, Vol. 45 (2004) pp Conference Proceedings Preprints Conference Abstract Wavelets and inverse problems (with Kavita Goyal), Mathematics in Science and Technology, Mathematical methods, models and algorithms in science and technology, Proceedings of Satellite conference of ICIAM 2011, (2011) pp Comparison Between Different Numerical Methods for Discretization of PDEs-A Short Review(with Nutan Patel and Rahul Kumar), AIP Conference Proceedings, Vol (2010) pp Wavelets and Differential equations-a short review, AIP Conference Proceedings, Vol (2009) pp A dynamic adaptive wavelet method for solution of the Schrodinger equation (with Ratikanta Behera) (Communicated). Fast diffusion wavelet method for partial differential equations (with Kavita Goyal) (Communicated). Diffusion wavelet based space time adaptive numerical method (with Kavita Goyal), at international conference on Mathematical Modelling and Computational Methods in Applied Sciences and Engineering, 2014, Roznov pod Radhostem, Czech Republic. An adaptive meshfree spectral graph wavelet method for partial differential equations on the sphere, (with Kavita Goyal), at 5th International Conference on Computational Harmonic Analysis, May, 2014, Vanderbilt University, Nashville, USA. Sparse evolutions of functions using diffusion wavelet (with Kavita Goyal), at International Conference on Applied Harmonic Analysis and Multiscale Computing, July 2011, University of Alberta, Edmonton, Canada. Adaptive wavelet collocation method for PDEs, at international workshop for Fluid and Plasma turbulence: Application to Magnetically Confined Plasmas in Fusion Devices, 2008, Marseille, France. An Adaptive wavelet collocation method for partial differential equations on the sphere (with Nicholas Kevlahan), at the CAIMS-MITAC joint annual conference, 2007, York University, Toronto, Canada. Poster on Error estimates for linear PDE s solved by wavelet based Taylor- Galerkin schemes, at the conference of Wavelet and Applications, 2006, EPFL, Switzerland. Error estimates for linear PDE s solved by wavelet based Taylor-Galerkin schemes, at the fifth international conference on Scientific Computing and Application, 2006, Banff, Alberta, Canada. Wavelet based Fast Time Accurate schemes for Partial Differential Equations (with B. V. Rathish Kumar), at third Montreal Scientific Computing Days, 2006, Montreal, Canada.
6 Poster on Krylov Subspace Solvers in Parallel Finite Computation of PDEs Modelling Convection in Wavy Porous Enclosures (with B. V. Rathish Kumar and Shalini), at the conference Recent Advances in Nonlinear Science, 2002, Indian Institute of Science, Bangalore, India. Wavelet Multilayer Taylor Galerkin schemes for Hyperbolic and Parabolic problems (with B. V. Rathish Kumar), at the 48th Congress of Indian Society of Theoretical and applied Mechanics, 2003, BIT Mesra, India. Krylov Solvers on Parallel Computers (with B. V. Rathish Kumar and Shalini), at the 48th Congress of Indian Society of Theoretical and applied Mechanics, 2003, BIT Mesra, India. A Wavelet Taylor Galerkin Method for Advection-Diffusion problems (with B. V. Rathish Kumar), at the 31st Conference of Orissa Mathematical Society, 2004, Orissa, India. Invited Talks Talks I: Introduction to wavelets Talk II: Wavelets based numerical methods for PDEs, 2013, Refresher course in Mathematics, Computer science, Statistics and Operation research, Delhi University, India. Hand on session on MATLAB, 2012, National Workshop and Training Program on Differential Equations and Mathematical Modeling [DEMM], Delhi University, India. Sparse evolution of functions using diffusion wavelets, 2011, ICIAM conference, Vancouver, Canada. Wavelets based numerical methods for PDEs, 2010 Workshops on Advanced Computing and Software Tools (ACST-2010), JIIT Noida, India. Wavelets and its applications, 2011, Workshop on Wavelets and Its Applications in Signal Processing, JIIT Noida, India. Application of wavelets to partial differential equations, at MODELLING OF ENGINEERING AND TECHNOLOGICAL PROBLEMS: International Conference on Modelling and Engineering and Technological Problems (ICMETP) and the 9th Biennial National Conference of Indian Society of Industrial and Applied Mathematics (ISIAM), 2009, Agra, India. Applications of wavelets to partial differential equations, 2007, Center for Atmospheric Science, Indian Institute of Science, Bangalore, India. Applications of wavelets to partial differential equations, 2007, Dept. of Mathematics, Tata institute of fundamental Research, Bangalore, India. Wavelet based Fast Time Accurate schemes for Partial Differential Equations, 2005, Dept. of Mathematics and Statistics, McMaster University, Canada. Adaptive wavelet collocation method for the partial differential equations on the sphere, 2006, Dept. of Mathematics and Statistics, McMaster University, Canada. Contributed Talks Adaptive wavelet collocation method for PDEs, at international workshop for Fluid and Plasma turbulence: Application to Magnetically Confined Plasmas in Fusion Devices, 2008, Marseille, France.
7 Error estimates for linear PDE s solved by wavelet based Taylor-Galerkin schemes, at the fifth international conference on Scientific Computing and Application, 2006, Banff, Alberta, Canada. Wavelet based Fast Time Accurate schemes for Partial Differential Equations, at third Montreal Scientific Computing Days, 2006, Montreal, Canada. Wavelet Multilayer Taylor Galerkin schemes for Hyperbolic and Parabolic problems, at the 48th Congress of Indian Society of Theoretical and applied Mechanics, 2003, BIT Mesra, India. Krylov Solvers on Parallel Computers, at the 48th Congress of Indian Society of Theoretical and applied Mechanics, 2003, BIT Mesra, India. A Wavelet Taylor Galerkin Method for Advection-Diffusion problems, at the 31st Conference of Orissa Mathematical Society, 2004, Orissa, India. Conferences Workshop Attended 10th International Conference on Sampling Theory and Applications, 2013, Bremen, Germany. 11th Biennial conference of ISIAM (Indian Society of the Industrial and Applied Mathematics), 2012, Gautam Buddha University, India. ICIAM, 2011, Vancouver, Canada. Wavelets and Its Applications in Signal Processing, 2011, JIIT Noida, India. Advanced Computing and Software Tools (ACST-2010), 2010, JIIT Noida, India. Inverse problems and wavelets with applications to real world system, 2010, IHC, New Delhi, India. Satellite conference of ICM2010 on Mathematics in Science and Technology, 2010, IHC, New Delhi, India. International Conference on Modelling and Engineering and Technological Problems (ICMETP) and the 9th Biennial National Conference of Indian Society of Industrial and Applied Mathematics (ISIAM), 2009, Agra, India. International workshop for Fluid and Plasma turbulence: Application to Magnetically Confined Plasmas in Fusion Devices, 2008, Marseille, France. Wave2006, 2006, EPFL, Switzerland. CAIMS-MITACS 2006 Joint Annual Conference, 2006, York. Univ., Toronto, Canada. Fifth international conference on Scientific Computing and Application, 2006, Banff, Alberta, Canada. Third Montreal Scientific Computing Days, 2006, Montreal, Canada. International Conference on Mathematical Biology, 2004, IIT-Kanpur, India. Recent Advances in Nonlinear Science, 2002 by Indian Institute of science, Bangalore, India. 48th Congress of Indian Society of Theoretical and applied Mechanics (An International Meet), 2003, BIT Mesra, India.
8 31st Conference of Orissa Mathematical Society, 2004, Bhubaneswar, India. National Workshop on Wavelet Analysis and Applications, 2004, Bhubaneswar, India. Education Indian Institute Of Technology, Kanpur, India. Ph.D. in Applied Mathematics (CPI 9.43/10): April Thesis Title: Wavelet based fast time accurate schemes and preconditioners for partial differential equations Thesis supervisor: Prof. B. V. Rathish Kumar Indian Institute of Technology, Roorkee, India. M.Sc. in Applied Mathematics (Gold Medalist with 86%), July Achievements and Scholarships Got the president of India cash prize for the best paper award in the 48th ISTAM held during 18-21, December 2003 at BITS Mesra, Ranchi,Bihar, India. Qualified Joint CSIR-UGC Eligibility for Lectureship-National Eligibility Test (All India Rank-among 50). Qualified All India Graduate Aptitude Test (GATE) 2000 ( The Indian equivalent of Subject GRE, conducted by The Indian Institute of Technology) with percentile, in 2000 (All India Rank-10). Gold Medal (Institute Medal) for standing first in first class M.Sc. Scholarship (in terms of waived fees) for standing first in first class M.Sc. Selected for national scholarship in Computation Languages: C, C++, FORTRAN 90. Skills Operating Systems: WINDOWS, LINUX. Softwares: MATLAB, MATHEMATICA, MS OFFICE, LATEX.
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Numerical Methods for Differential Equations Course objectives and preliminaries Gustaf Söderlind and Carmen Arévalo Numerical Analysis, Lund University Textbooks: A First Course in the Numerical Analysis
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