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Water Surface Elevation at i'th step in Standard Fourth-Order Runge-Kutta Method Formula

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Water Surface Elevation at i'th Step in standard fourth order runge-kutta method. Check FAQs

H i = H i+1 - ((\frac{1}{6}) \cdot (K 1 + 2 \cdot K 2 + 2 \cdot K 3 + K 4) \cdot Δt)

H_i - Water Surface Elevation at i'th Step?H_i+1 - Water Surface Elevation at (i+1)th Step?K₁ - Coefficient K1 by Repeated Appropriate Evaluation?K₂ - Coefficient K2 by Repeated Appropriate Evaluation?K₃ - Coefficient K3 by Repeated Appropriate Evaluation?K₄ - Coefficient K4 by Repeated Appropriate Evaluation?Δt - Time Interval?

Water Surface Elevation at i'th step in Standard Fourth-Order Runge-Kutta Method Example

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Here is how the Water Surface Elevation at i'th step in Standard Fourth-Order Runge-Kutta Method equation looks like with Values.

Here is how the Water Surface Elevation at i'th step in Standard Fourth-Order Runge-Kutta Method equation looks like with Units.

Here is how the Water Surface Elevation at i'th step in Standard Fourth-Order Runge-Kutta Method equation looks like.

10 = 18 - ((\frac{1}{6}) \cdot (1.61 + 2 \cdot 1.98 + 2 \cdot 1.28 + 1.47) \cdot 5)

10 = 18 - ((\frac{1}{6}) \cdot (1.61 + 2 \cdot 1.98 + 2 \cdot 1.28 + 1.47) \cdot 5s)

10 = 18 - ((\frac{1}{6}) \cdot (1.61 + 2 \cdot 1.98 + 2 \cdot 1.28 + 1.47) \cdot 5)

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Water Surface Elevation at i'th step in Standard Fourth-Order Runge-Kutta Method Solution

Follow our step by step solution on how to calculate Water Surface Elevation at i'th step in Standard Fourth-Order Runge-Kutta Method?

FIRST Step Consider the formula

H i = H i+1 - ((\frac{1}{6}) \cdot (K 1 + 2 \cdot K 2 + 2 \cdot K 3 + K 4) \cdot Δt)

Next Step Substitute values of Variables

∴

H i = 18 - ((\frac{1}{6}) \cdot (1.61 + 2 \cdot 1.98 + 2 \cdot 1.28 + 1.47) \cdot 5s)

Next Step Prepare to Evaluate

∴

H i = 18 - ((\frac{1}{6}) \cdot (1.61 + 2 \cdot 1.98 + 2 \cdot 1.28 + 1.47) \cdot 5)

LAST Step Evaluate

∴

H i = 10

Water Surface Elevation at i'th step in Standard Fourth-Order Runge-Kutta Method Formula Elements

Variables

Water Surface Elevation at i'th Step

Water Surface Elevation at i'th Step in standard fourth order runge-kutta method.

Symbol: H_i

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Water Surface Elevation at (i+1)th Step

Water Surface Elevation at (i+1)th Step in standard fourth order runge-kutta method.

Symbol: H_i+1

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Coefficient K1 by Repeated Appropriate Evaluation

Coefficient K1 by Repeated Appropriate Evaluation of the function F(t, H).

Symbol: K₁

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Coefficient K2 by Repeated Appropriate Evaluation

Coefficient K2 by Repeated Appropriate Evaluation of the function F(t, H).

Symbol: K₂

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Coefficient K3 by Repeated Appropriate Evaluation

Coefficient K3 by Repeated Appropriate Evaluation of the function F(t, H).

Symbol: K₃

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Coefficient K4 by Repeated Appropriate Evaluation

Coefficient K4 by Repeated Appropriate Evaluation of the function F(t, H).

Symbol: K₄

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Time Interval

Time Interval is the amount of time required for the change from the initial to the final state.

Symbol: Δt

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Credits

Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

Mithila Muthamma PA has created this Formula and 2000+ more formulas!

Verified by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has verified this Formula and 1700+ more formulas!

Other formulas in Standard Fourth Order Range Kutta Method category

Go Water Surface Elevation in Standard Fourth-Order Runge-Kutta Method

H i+1 = H i + (\frac{1}{6}) \cdot (K 1 + 2 \cdot K 2 + 2 \cdot K 3 + K 4) \cdot Δt

How to Evaluate Water Surface Elevation at i'th step in Standard Fourth-Order Runge-Kutta Method?

Water Surface Elevation at i'th step in Standard Fourth-Order Runge-Kutta Method evaluator uses Water Surface Elevation at i'th Step = Water Surface Elevation at (i+1)th Step-((1/6)*(Coefficient K1 by Repeated Appropriate Evaluation+2*Coefficient K2 by Repeated Appropriate Evaluation+2*Coefficient K3 by Repeated Appropriate Evaluation+Coefficient K4 by Repeated Appropriate Evaluation)*Time Interval) to evaluate the Water Surface Elevation at i'th Step, Water Surface Elevation at i'th step in Standard Fourth-Order Runge-Kutta Method is defined as the computations for the elevation of the water surface or depth of flow by Repeated Appropriate Evaluation of the function F(t, H) . Water Surface Elevation at i'th Step is denoted by H_i symbol.

How to evaluate Water Surface Elevation at i'th step in Standard Fourth-Order Runge-Kutta Method using this online evaluator? To use this online evaluator for Water Surface Elevation at i'th step in Standard Fourth-Order Runge-Kutta Method, enter Water Surface Elevation at (i+1)th Step (H_i+1), Coefficient K1 by Repeated Appropriate Evaluation (K₁), Coefficient K2 by Repeated Appropriate Evaluation (K₂), Coefficient K3 by Repeated Appropriate Evaluation (K₃), Coefficient K4 by Repeated Appropriate Evaluation (K₄) & Time Interval (Δt) and hit the calculate button.

FAQs on Water Surface Elevation at i'th step in Standard Fourth-Order Runge-Kutta Method

What is the formula to find Water Surface Elevation at i'th step in Standard Fourth-Order Runge-Kutta Method?

The formula of Water Surface Elevation at i'th step in Standard Fourth-Order Runge-Kutta Method is expressed as Water Surface Elevation at i'th Step = Water Surface Elevation at (i+1)th Step-((1/6)*(Coefficient K1 by Repeated Appropriate Evaluation+2*Coefficient K2 by Repeated Appropriate Evaluation+2*Coefficient K3 by Repeated Appropriate Evaluation+Coefficient K4 by Repeated Appropriate Evaluation)*Time Interval). Here is an example- 10 = 18-((1/6)*(1.61+2*1.98+2*1.28+1.47)*5).

How to calculate Water Surface Elevation at i'th step in Standard Fourth-Order Runge-Kutta Method?

With Water Surface Elevation at (i+1)th Step (H_i+1), Coefficient K1 by Repeated Appropriate Evaluation (K₁), Coefficient K2 by Repeated Appropriate Evaluation (K₂), Coefficient K3 by Repeated Appropriate Evaluation (K₃), Coefficient K4 by Repeated Appropriate Evaluation (K₄) & Time Interval (Δt) we can find Water Surface Elevation at i'th step in Standard Fourth-Order Runge-Kutta Method using the formula - Water Surface Elevation at i'th Step = Water Surface Elevation at (i+1)th Step-((1/6)*(Coefficient K1 by Repeated Appropriate Evaluation+2*Coefficient K2 by Repeated Appropriate Evaluation+2*Coefficient K3 by Repeated Appropriate Evaluation+Coefficient K4 by Repeated Appropriate Evaluation)*Time Interval).

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Water Surface Elevation at i'th step in Standard Fourth-Order Runge-Kutta Method Formula

Water Surface Elevation at i'th step in Standard Fourth-Order Runge-Kutta Method Example

Water Surface Elevation at i'th step in Standard Fourth-Order Runge-Kutta Method Solution

Water Surface Elevation at i'th step in Standard Fourth-Order Runge-Kutta Method Formula Elements

Credits

Other formulas in Standard Fourth Order Range Kutta Method category

How to Evaluate Water Surface Elevation at i'th step in Standard Fourth-Order Runge-Kutta Method?

FAQs on Water Surface Elevation at i'th step in Standard Fourth-Order Runge-Kutta Method

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