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gptkbp:instanceOf
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gptkb:algorithm
gptkb:logic
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gptkbp:application
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numerical integration
simulation of dynamical systems
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gptkbp:category
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initial value problem
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gptkbp:error_order
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O(h^2)
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gptkbp:field
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gptkb:mathematics
numerical analysis
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gptkbp:firstPublished
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1768
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gptkbp:global_error_order
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O(h)
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https://www.w3.org/2000/01/rdf-schema#label
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Euler method
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gptkbp:input
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partial differential equations
initial condition
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gptkbp:limitation
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low accuracy for stiff equations
numerical instability for large step sizes
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gptkbp:main_formula
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y_{n+1} = y_n + h f(x_n, y_n)
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gptkbp:namedAfter
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gptkb:Leonhard_Euler
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gptkbp:order_of_accuracy
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first order
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gptkbp:output
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approximate solution at discrete points
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gptkbp:relatedTo
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gptkb:Runge-Kutta_methods
gptkb:Heun's_method
gptkb:backward_Euler_method
gptkb:improved_Euler_method
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gptkbp:step_size
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h
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gptkbp:type
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explicit method
local truncation error
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gptkbp:usedFor
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solving ordinary differential equations
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gptkbp:bfsParent
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gptkb:Runge-Kutta_methods
gptkb:Numerical_Solution_of_Differential_Equations
gptkb:Fourth-order_Runge–Kutta_method
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gptkbp:bfsLayer
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7
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