Results 251 to 260 of about 2,445,513 (291)
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1966
Publisher Summary This chapter focuses on higher-order linear equations. Even for second-order linear equations, no general method of solution is available as there was for first-order equations. Formulas for general solutions can be found for certain special classes of higher-order equations.
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Publisher Summary This chapter focuses on higher-order linear equations. Even for second-order linear equations, no general method of solution is available as there was for first-order equations. Formulas for general solutions can be found for certain special classes of higher-order equations.
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Ordinary Differential Equations
2012In this chapter we provide an overview of the basic theory of ordinary differential equations (ODE). We give the basics of analytical methods for their solutions and also review numerical methods. The chapter should serve as a primer for the basic application of ODEs and systems of ODEs in practice.
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On the Stability of Differential Equations
SIAM Journal on Control, 1972A polynomial is said to be of type $(p_1 ,p_2 ,p_3 )$ relative to any directed line in the complex plane if it has $p_1 $ zeros to the left of, $p_2 $ on, and $p_3 $ to the right of the line.
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2011
This chapter introduces numerical methods that can be used on problems that are too hard to solve by standard algebra, such as finding roots of complicated equations. It demonstrates numerical methods for solving a first-order ordinary differential equations (ODE) with an initial condition.
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This chapter introduces numerical methods that can be used on problems that are too hard to solve by standard algebra, such as finding roots of complicated equations. It demonstrates numerical methods for solving a first-order ordinary differential equations (ODE) with an initial condition.
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DeepXDE: A Deep Learning Library for Solving Differential Equations
SIAM Review, 2021Lu Lu, George Karniadakis, Xuhui Meng
exaly
Solving high-dimensional partial differential equations using deep learning
Proceedings of the National Academy of Sciences of the United States of America, 2018Jiequn Han, Arnulf Jéntzen, Weinan E
exaly
Analysis of Fractional Differential Equations
Journal of Mathematical Analysis and Applications, 2002Kai Diethelm, Neville Ford
exaly