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

✖Water Surface Elevation at i'th Step in standard fourth order runge-kutta method.ⓘ Water Surface Elevation at i'th Step [H_i]			+10% -10%
✖Coefficient K1 by Repeated Appropriate Evaluation of the function F(t, H).ⓘ Coefficient K1 by Repeated Appropriate Evaluation [K₁]			+10% -10%
✖Coefficient K2 by Repeated Appropriate Evaluation of the function F(t, H).ⓘ Coefficient K2 by Repeated Appropriate Evaluation [K₂]			+10% -10%
✖Coefficient K3 by Repeated Appropriate Evaluation of the function F(t, H).ⓘ Coefficient K3 by Repeated Appropriate Evaluation [K₃]			+10% -10%
✖Coefficient K4 by Repeated Appropriate Evaluation of the function F(t, H).ⓘ Coefficient K4 by Repeated Appropriate Evaluation [K₄]			+10% -10%
✖Time Interval is the amount of time required for the change from the initial to the final state.ⓘ Time Interval [Δt]			+10% -10%

✖Water Surface Elevation at (i+1)th Step in standard fourth order runge-kutta method.ⓘ Water Surface Elevation in Standard Fourth-Order Runge-Kutta Method [H_i+1]

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Formula

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

Formula

`"H"_{"i+1"} = "H"_{"i"}+(1/6)*("K"_{"1"}+2*"K"_{"2"}+2*"K"_{"3"}+"K"_{"4"})*"Δt"`

Example

`"18"="10.0"+(1/6)*("1.61"+2*"1.98"+2*"1.28"+"1.47")*"5s"`

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

STEP 0: Pre-Calculation Summary

Formula Used

Water Surface Elevation at (i+1)th Step = Water Surface Elevation at i'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
H_i+1 = H_i+(1/6)*(K₁+2*K₂+2*K₃+K₄)*Δt
This formula uses 7 Variables

Variables Used

Water Surface Elevation at (i+1)th Step - Water Surface Elevation at (i+1)th Step in standard fourth order runge-kutta method.
Water Surface Elevation at i'th Step - Water Surface Elevation at i'th Step in standard fourth order runge-kutta method.
Coefficient K1 by Repeated Appropriate Evaluation - Coefficient K1 by Repeated Appropriate Evaluation of the function F(t, H).
Coefficient K2 by Repeated Appropriate Evaluation - Coefficient K2 by Repeated Appropriate Evaluation of the function F(t, H).
Coefficient K3 by Repeated Appropriate Evaluation - Coefficient K3 by Repeated Appropriate Evaluation of the function F(t, H).
Coefficient K4 by Repeated Appropriate Evaluation - Coefficient K4 by Repeated Appropriate Evaluation of the function F(t, H).
Time Interval - (Measured in Second) - Time Interval is the amount of time required for the change from the initial to the final state.

STEP 1: Convert Input(s) to Base Unit

Water Surface Elevation at i'th Step: 10 --> No Conversion Required
Coefficient K1 by Repeated Appropriate Evaluation: 1.61 --> No Conversion Required
Coefficient K2 by Repeated Appropriate Evaluation: 1.98 --> No Conversion Required
Coefficient K3 by Repeated Appropriate Evaluation: 1.28 --> No Conversion Required
Coefficient K4 by Repeated Appropriate Evaluation: 1.47 --> No Conversion Required
Time Interval: 5 Second --> 5 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

H_i+1 = H_i+(1/6)*(K₁+2*K₂+2*K₃+K₄)*Δt --> 10+(1/6)*(1.61+2*1.98+2*1.28+1.47)*5

Evaluating ... ...

H_i+1 = 18

STEP 3: Convert Result to Output's Unit

18 --> No Conversion Required

FINAL ANSWER

18 <-- Water Surface Elevation at (i+1)th Step

(Calculation completed in 00.004 seconds)

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Coorg Institute of Technology (CIT), Coorg

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< 2 Standard Fourth-Order Range Kutta Method Calculators

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

Go 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)

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

Go Water Surface Elevation at (i+1)th Step = Water Surface Elevation at i'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

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

Why Runge Kutta Method is used?

Runge–Kutta method is an effective and widely used method for solving the initial-value problems of differential equations. Runge–Kutta method can be used to construct high-order accurate numerical methods by functions' self without needing the high-order derivatives of functions.

Define Wave Height.

The wave height of a surface wave is the difference between the elevations of a crest and a neighbouring trough. Wave height is a term used by mariners, as well as in coastal, ocean and naval engineering.

How to Calculate Water Surface Elevation in Standard Fourth-Order Runge-Kutta Method?

Water Surface Elevation in Standard Fourth-Order Runge-Kutta Method calculator uses Water Surface Elevation at (i+1)th Step = Water Surface Elevation at i'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 calculate the Water Surface Elevation at (i+1)th Step, The Water Surface Elevation in Standard Fourth-Order Runge-Kutta Method formula 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) at (i+1)th step. Water Surface Elevation at (i+1)th Step is denoted by H_i+1 symbol.

How to calculate Water Surface Elevation in Standard Fourth-Order Runge-Kutta Method using this online calculator? To use this online calculator for Water Surface Elevation in Standard Fourth-Order Runge-Kutta Method, enter Water Surface Elevation at i'th Step (H_i), 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. Here is how the Water Surface Elevation in Standard Fourth-Order Runge-Kutta Method calculation can be explained with given input values -> 18 = 10+(1/6)*(1.61+2*1.98+2*1.28+1.47)*5.

FAQ

What is Water Surface Elevation in Standard Fourth-Order Runge-Kutta Method?

The Water Surface Elevation in Standard Fourth-Order Runge-Kutta Method formula 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) at (i+1)th step and is represented as H_i+1 = H_i+(1/6)*(K₁+2*K₂+2*K₃+K₄)*Δt or Water Surface Elevation at (i+1)th Step = Water Surface Elevation at i'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. Water Surface Elevation at i'th Step in standard fourth order runge-kutta method, Coefficient K1 by Repeated Appropriate Evaluation of the function F(t, H), Coefficient K2 by Repeated Appropriate Evaluation of the function F(t, H), Coefficient K3 by Repeated Appropriate Evaluation of the function F(t, H), Coefficient K4 by Repeated Appropriate Evaluation of the function F(t, H) & Time Interval is the amount of time required for the change from the initial to the final state.

How to calculate Water Surface Elevation in Standard Fourth-Order Runge-Kutta Method?

The Water Surface Elevation in Standard Fourth-Order Runge-Kutta Method formula 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) at (i+1)th step is calculated using Water Surface Elevation at (i+1)th Step = Water Surface Elevation at i'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 calculate Water Surface Elevation in Standard Fourth-Order Runge-Kutta Method, you need Water Surface Elevation at i'th Step (H_i), 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). With our tool, you need to enter the respective value for Water Surface Elevation at i'th Step, Coefficient K1 by Repeated Appropriate Evaluation, Coefficient K2 by Repeated Appropriate Evaluation, Coefficient K3 by Repeated Appropriate Evaluation, Coefficient K4 by Repeated Appropriate Evaluation & Time Interval and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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