Results 211 to 220 of about 11,797 (246)
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1995
As shown by equations (1.1.1–2), there is a close relationship between ordinary differential equations and Volterra integral equations. First, we discuss the unique solvability. Afterwards, in §2.1.2, we discuss the regularity of the solution.
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As shown by equations (1.1.1–2), there is a close relationship between ordinary differential equations and Volterra integral equations. First, we discuss the unique solvability. Afterwards, in §2.1.2, we discuss the regularity of the solution.
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Positive quadratures for volterra equations
Computing, 1976The present paper deals with discretizations to linear Volterra equations which preserve the possible positivity of the Volterra operator. It is shown that the method must be implicit and e.g. that the repeated trapezoidal rule has this property. It is then shown how this property can be used in studying the asymptotic behaviour of the solutionsx
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1970
In this chapter we investigate operator equations and inequalities for functions of one real variable. Our particular objective here is nonlinear Volterra integral equations and ordinary differential equations. Unless explicitly stated otherwise, the Lebesgue concept of integral is always presupposed.
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In this chapter we investigate operator equations and inequalities for functions of one real variable. Our particular objective here is nonlinear Volterra integral equations and ordinary differential equations. Unless explicitly stated otherwise, the Lebesgue concept of integral is always presupposed.
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2016
In this chapter, we conducted a thorough examination of the Volterra integral equation of the second kind for an arbitrary real parameter λ, assuming that the free term f (x) is real-valued and continuous on the interval [a, b] and that the kernel K(x, t) is real-valued, continuous, and separable on the square Q(a, b) = {(x, t): [a, b] × [a, b]}.
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In this chapter, we conducted a thorough examination of the Volterra integral equation of the second kind for an arbitrary real parameter λ, assuming that the free term f (x) is real-valued and continuous on the interval [a, b] and that the kernel K(x, t) is real-valued, continuous, and separable on the square Q(a, b) = {(x, t): [a, b] × [a, b]}.
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On a diffusion volterra equation
Nonlinear Analysis: Theory, Methods & Applications, 1979INTRODUCTION IN THIS paper we study the Volterra diffusion equation au/at = Au + au bu2 u(f*u)t (0.1 a) describing the evolution of some population governed by the intrinsic rate a bu and the memory rate f * u containing the effect of the past history on the actual population development.
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Solving integral equations in free space with inverse-designed ultrathin optical metagratings
Nature Nanotechnology, 2023Andrea Cordaro, Andrea Alu
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DeepXDE: A Deep Learning Library for Solving Differential Equations
SIAM Review, 2021Lu Lu, George E Karniadakis
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New Creatinine- and Cystatin C–Based Equations to Estimate GFR without Race
New England Journal of Medicine, 2021Lesley A Inker +2 more
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