This paper investigates singularly perturbed parabolic partial differential equations
with delay in space, and the right end plane is an integral boundary condition on a
rectangular domain. A small parameter is multiplied in the higher order derivative,
which gives boundary layers, and due to the delay term, one more layer occurs on the
rectangle domain. A numerical method comprising the standard finite difference
scheme on a rectangular piecewise uniform mesh (Shishkin mesh) of Nr ×Nt
elements condensing in the boundary layers is suggested, and it is proved to be
parameter-uniform. Also, the order of convergence is proved to be almost two in
space variable and almost one in time variable. Numerical examples are proposed to
validate the theory.
Sample Chapter(s)
Preface (73 KB)
Components of the Book:
- Chapter 1
Dynamic Deformation Measurement by the Sampling Moiré Method from Video Recording and its Application to Bridge Engineering
- Chapter 2
Existence results for infinite systems of the Hilfer fractional boundary value problems in Banach sequence spaces
- Chapter 3
Finite difference scheme for singularly perturbed reaction diffusion problem of partial delay differential equation with nonlocal boundary condition
- Chapter 4
New Hermite–Hadamard-type inequalities for (h1, h2)-convex fuzzy-interval-valued functions
- Chapter 5
Study of a nonlinear multi-terms boundary value problem of fractional pantograph differential equations
- Chapter 6
Optimal control of nonlocal fractional evolution equations in the α-norm of order (1, 2)
- Chapter 7
Novel existence techniques on the generalized ϕ-Caputo fractional inclusion boundary problem
- Chapter 8
On a system of Riemann–Liouville fractional differential equations with coupled nonlocal boundary conditions
- Chapter 9
Oscillation criteria for difference equations with non-monotone arguments
- Chapter 10
On nonlocal fractional sum-difference boundary value problems for Caputo fractional functional difference equations with delay
- Chapter 11
Asymptotic behavior of mild solutions for a class of abstract nonlinear difference equations of convolution type
- Chapter 12
On the multiple-scale analysis for some linear partial q-difference and differential equations with holomorphic coefficients
- Chapter 13
Hahn difference equations in Banach algebras
- Chapter 14
On sequences of large homoclinic solutions for a difference equations on the integers
- Chapter 15
Existence and Ulam stability for implicit fractional q-difference equations
Readership:
Students, academics, teachers and other people attending or interested in difference equations.
Sekar Elango
Department of Mathematics, SASTRA Deemed to be University, Thanjavur,Tamilnadu, India
Thomas Dreyfus
IRMA, Université de Strasbourg, Strasbourg, France
Jehad Alzabut
Department of Mathematics and General Sciences, Prince Sultan University, Riyadh,Saudi Arabia
Rodica Luca
Department of Mathematics, Gh. Asachi Technical University, 11 Blvd. Carol I, nr. 11, Iasi, Romania
George E Chatzarakis
Department of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education (ASPETE), N. Heraklio, Athens, 14121, Greece
and more...