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Devendra Kumar 

Professor, Department of Mathematics,
BITS Pilani, Pilani Campus

Numerical solutions of ODEs & PDEs, Singular perturbations
Department of Mathematics, Birla Institute of Technology & Science, Pilani- 333031, Rajasthan. India.

Research Interest

 

My research interest includes the development of the numerical methods for the singularly perturbed boundary value problems arising in many applications of science and engineering. Singularly perturbed boundary value problems are those in which the highest order derivative is multiplied by a small parameter ε, known as the perturbation parameter. As ε → 0, the order of the differential equation reduces by at least one and so the solution to the reduced problem fails to satisfy all the boundary conditions. Thus as ε → 0, the solution to these problems has multiple behaviors in the sense that there are the regions where solution changes very rapidly (these regions are called layer regions) otherwise the solution varies slowly (these regions are called outer regions). The classical/standard numerical methods fail to approximate the solution to these problems, so we need to develop non-classical/nonstandard methods for the solution of these problems.

In particular, my research includes the development of the numerical methods for Initial/Boundary Value Problems for Ordinary Differential Equations, Partial Differential Equations, Delay/Advanced Differential Equations, Singularly Perturbed ODEs/PDEs, Fractional Order ODEs/PDEs etc.


Teaching

 

Courses in Current Semester

  • Mathematics II (MATH F112)
  • Partial Differential Equations (MATH F343)

Courses Taught


On Campus

  • Mathematics I (MATH F111)
  • Mathematics II (MATH F112)
  • Mathematics III (MATH F211)
  • Probability and Statistics (MATH F113)
  • Mathematical Methods (MATH F241)
  • Numerical Analysis (MATH F313)
  • Partial Differential Equations (MATH F343)
  • Numerical Methodology for Partial Differential Equations (MATH F422)
  • Numerical Solutions to Ordinary Differential Equations (MATH F444)

 


Off-Campus

  • Engineering Mathematics I
  • Engineering Mathematics II