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Understanding Structural Equation Modeling A Manual for Researchers
This book presents a comprehensive overview of Structural Equation Modeling and how it can be applied to address research issues in different...
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The Diffusion Equation
The diffusion equation appears in many applications in science and engineering, and computational physiology is no exception. In its most basic form,...
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The Heat Equation
This chapter deals with the heat equation. They are considered the weak and strong maximum principles, the Cauchy problem, the mean value formula,...
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A Simple Cable Equation
The cable equation was first derived to model transport of electrical signals in telegraphic cables. But it later gained enormous popularity as a...
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Many-Body Schrödinger Equation Scattering Theory and Eigenfunction Expansions
Spectral properties for Schrödinger operators are a major concern in quantum mechanics both in physics and in mathematics. For the few-particle...
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Solving A Nonlinear Equation
In this chapter, one of the more common mathematical problems is studied, which is to find the solution, or solutions, of an equation of the form...
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Nonlinear Perturbed BLMP Equation
In the present paper we consider the non-existence of weak solutions related to a class of differential equations connected with the Airy operator....
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The Microscope Equation
If we are in a car and we look at the speedometer and it says we are traveling 60 mph, then about how far will we travel in the next minute? 30...
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A Difference Scheme for Wave Equation
AbstractThe paper deals with a numerical solution of a wave equation. The solution algorithm uses optimal parameters which are obtained by using...
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Parareal Algorithms for the Cahn-Hilliard Equation
In this work we are interested in designing time parallel algorithm for the Cahn-Hilliard (CH) equation.
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Solving Non-linear Fractional Coupled Burgers Equation by Sub-equation Method
In this solution, the real results were reached in solving the nonlinear fractional Coupled Burgers equation, which represents the solution with...
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Propagation of Singularities for the Wave Equation
This expository note gives a digest version of Hörmander’s propagation of singularities theorem for the wave equation.
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Darboux Transformation and Exact Solution for Novikov Equation
In this paper, the lax pair of Novikov equation is given in 3 \(\times \)...
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Lagrangians, SO(3)-Instantons and Mixed Equation
The mixed equation , defined as a combination of the anti-self-duality equation in gauge theory and Cauchy–Riemann equation in symplectic geometry, is...
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Pál–Bell Equation and Moment Growth
The previous chapter largely dealt with the relationship between the NTE and the NBP. The NTE is a linear equation and so there is limited...
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On Singular Heat Equation
AbstractIn physics, the singular heat equation with the Bessel operator is used to explain the basic process of heat transport in a substance with...
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The Sylvester Equation
Consider the operator equation: \(\displaystyle AX-XB=C, \)...
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On a Forward and a Backward Stochastic Euler Equation
We derive a stochastic Euler equation with transport noise and terminal time condition from a variational principle and relate it to the...
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A Cauchy Problem for q-Heat Equation
In this paper, we explore the weak solutions of the Cauchy problem and an inverse source problem for the heat equation in the quantum calculus,...
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A Natural Full-Discretization of the Korteweg-de-Vries Equation
In this paper, we propose an integrable full-discretization of the Korteweg-de-Vries (KdV) equation. Our method is based on the compatibility between...